Explanation:
It is given that,
Mass of the car 1, [tex]m_1=900\ kg[/tex]
Initial speed of car 1, [tex]u_1=15i\ m/s[/tex] (east)
Mass of the car 2, [tex]m_2=750\ kg[/tex]
Initial speed of car 2, [tex]u_1=20j\ m/s[/tex] (north)
(b) As the cars stick together. It is a case of inelastic collision. Let V is the common speed after the collision. Using the conservation of momentum as :
[tex]m_1u_1+m_2u_2=(m_1+m_2)V[/tex]
[tex]900\times 15i +750\times 20j=(900+750)V[/tex]
[tex]13500i+15000j=1650V[/tex]
[tex]V=(8.18i+9.09j)\ m/s[/tex]
The magnitude of speed,
[tex]|V|=\sqrt{8.18^2+9.09^2}[/tex]
V = 12.22 m/s
(b) Let [tex]\theta[/tex] is the direction the wreckage move just after the collision. It is given by :
[tex]tan\theta=\dfrac{v_y}{v_x}[/tex]
[tex]tan\theta=\dfrac{9.09}{8.18}[/tex]
[tex]\theta=48.01^{\circ}[/tex]
Hence, this is the required solution.
To solve this problem, we can use the principle of conservation of momentum. We calculate the momentum of each car before the collision, then find the total momentum before the collision. Since the cars stick together after the collision, we can calculate the velocity of the wreckage and determine its direction using trigonometry.
Explanation:To solve this problem, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
First, we need to calculate the momentum of each car before the collision. The momentum is calculated by multiplying the mass of the car by its velocity. Next, we can calculate the total momentum before the collision by adding up the individual momenta of the two cars. Since the cars stick together after the collision, we can find the velocity of the wreckage by dividing the total momentum by the total mass of the cars. Finally, we can use trigonometry to find the direction of the wreckage's motion. We have the x-component and y-component of the velocity, so we can use these values to calculate the direction. Learn more about Conservation of momentum here:https://brainly.com/question/33316833
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For which of the following situations is the conservation of mechanical energy most likely to be a valid assumption?a. a skateboard rolls across a sewer grate
b. a parachutist falls from a plane
c. you rub your hands together to keep warm
d. a soccer ball flies through the air
Answer: Option c is Correct!
You rub your hands together to keep warm.
Explanation:
First and foremost, mechanical energy is the sum of kinetic energy and potential energy of a system.
M.E = K.E + P.E
Where;
M.E= Mechanical energy
K.E= Kinetic energy
P.E= Potential energy
The kinetic energy is the energy possesed by a moving body, while the Potential energy is possesed by a stationary body.
When you rub your hand together to produce heat that keeps you warm, there is conservation of energy.
According to the first law of thermodynamics also known as the energy conservation law: it states that energy can neither be created nor destroyed, but can be transformed from one form to another.
The rubbing of the hand creates a motion(Kinetic energy) between the palms, this motion is opposed by a force called friction. thus the generation of heat accounts for the transfer of energy from Kinetic to Heat energy, therefore Mechanical energy is conserved according to the law of thermodynamics
What symbol is used to represent internal energy in the first law of thermodynamics?
A. Q
B. W
C. U
D. V
Answer:
\Delta U = Q - W
aka—^
(ΔU = Q − W)
The symbol for Internal Energy Change isΔU. It is the sum of all the microscopic energies such as: translational kinetic energy. vibrational and rotational kinetic energy.
Answer:
C. U
Explanation:
HOPE THAT HELPS :)
If a motor neuron involved in a reflex arc is damaged, which event in that arc is least likely to occur?
Final answer:
If a motor neuron involved in a reflex arc is damaged, the event that is least likely to occur is the muscle contraction in response to the sensory stimulus.
Explanation:
If a motor neuron involved in a reflex arc is damaged, the event that is least likely to occur is the muscle contraction in response to the sensory stimulus. In a reflex arc, the motor neuron carries the impulse from the interneuron to the muscle, causing it to contract. If the motor neuron is damaged, this communication pathway is disrupted, and the muscle will not receive the signal to contract.
A particle of mass 4.00 kg is attached to a spring with a force constant of 100 N/m. It is oscillating on a frictionless, horizontal surface with an amplitude of 2.00 m. A 6.00-kg object is dropped vertically on top of the 4.00-kg object as it passes through its equilibrium point. The two objects stick together.
a. Does the amplitude of the vibrating system increase or decrease as a result of the collision? By how much does the amplitude of the vibrating system change as a result of the collision?
b. How does the period change? By how much does the period change?
c. How does the mechanical energy of the system change? By how much does the energy change?
d. Account for the change in energy.
The amplitude and mechanical energy of the vibrating system decrease as a result of the collision, while the period increases. The decrease in mechanical energy is due to some kinetic energy being converted into heat and sound during the collision.
Explanation:a. The amplitude of the vibrating system decreases. Since kinetic energy is conserved, and the total mass is now larger (6.00 kg + 4.00 kg = 10.00 kg), the amplitude decreases. The new amplitude is equal to the original amplitude multiplied by the ratio of the original mass to total mass (4.00 kg / 10.00 kg) after the collision. Hence, the new amplitude is 2.00 m * 4.00 kg / 10.00 kg = 0.80 m.
b. The period of the oscillation increases as a result of the collision. The period (T) of oscillation is given by T = 2*π*(m/K)^(1/2), where K is the spring constant and m is the total mass. The mass is now larger (10.00 kg) leading to an increase in the period. As period depends on the root of the mass, the new period isn't directly proportional to the change in mass.
c. The mechanical energy of the system decreases as a result of the collision. This is because during the collision, some kinetic energy is lost and converted into heat and sound. Exact change in energy depends on how much energy is converted in these forms.
d. The change in energy can be accounted for by considering conservation of energy. Energy is never lost or gained, merely transformed from one form to another. In this case, the mechanical energy of the system decreased because some of it got converted into heat and sound during collision.
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A car travels over a dirt road that contains a series of equally spaced bumps (a so-called "washboard" road). While traveling at a given speed the driver experiences a very jarring ride. When the driver drives at a higher speed, however, the ride gets smoother. That is because
Answer:
Explanation:
When a car moves faster then it made suspension to oscillate at a faster rate than the previous frequency. The comfort of the car depends upon the natural frequency of suspension. A low frequency can give discomfort while the high frequency can also be harsh. An optimum frequency matching the level of human comfort is desired in the suspension system to absorb the shock.
The ride is perceived as comfortable when the natural frequency is at the level of 60 to 90 cycles per minute.
Which of the following best describes the human population from early times to the present?
Answer:
We have a not significant increase of the population until 1700s or 1800s and then a significant increase growth from these years to the present.
Explanation:
From the figure attached we see the evolution of the human population since early times (1050).
We see that from 1050 until 1750-1850 we have an increase slowly with a low value for the increase per year.
But after these years (1750-1850) we see a considerable increase of the population, like an exponential model.
So then we can conclude in general terms this:
We have a not significant increase of the population until 1700s or 1800s and then a significant increase growth from these years to the present.
The growth of the human population from early times to the present is best described by the Exponential Growth Model, which shows a rapid increase in population over time. It took 123 years to add 1 billion people between 1804 and 1930 and only 24 years to add 2 billion people between 1975 and 1999.
The best mathematical model that describes the growth of the human population from early times to the present is the Exponential Growth Model. Exponential growth occurs when a quantity increases exponentially over time, and this is evident in the rapid increase in the global population over centuries. The provided information shows that it took 123 years to add 1 billion people between 1804 and 1930, but only 24 years to add 2 billion people between 1975 and 1999.
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The probable question may be:
Over the course of history, the human population has experienced significant growth. Starting from an estimated 5 million people in the year 10,000 BCE, it is believed that the population has increased exponentially over the centuries. In 2021, the global population was approximately 7.8 billion.
Based on this data, which of the following mathematical models best describes the growth of the human population from early times to the present?
A) Linear Growth Model
B) Exponential Growth Model
C) Logarithmic Growth Model
D) Polynomial Growth Model
How is work related to potential energy and kinetic energy?
Work is defined as the force acting on an object because it changes a distance. While work is done on an object, the potential energy can be stored in that object. Thus, the relationship between work and energy is direct because the difference in kinetic energy of an object is the work done by the object.
What is Work done?Work done by a force is defined as the product of displacement and the component of force exerted by the object in the direction of displacement, thus when we push a block with some force the body starts moving with some acceleration moves, that's why the work is done.
Some transfer of energy may occur in the method of force where the amount of energy transferred by a force to move an object is called the work done.
Potential energy and work done are the same as kinetic energy and work done because potential energy is a state of the system, a way of storing energy as a property of its configuration or motion, while work is done in most cases there is a way to convert this energy from one body to another which is known as kinetic energy
Thus, Work is defined as the force acting on an object because it changes a distance.
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The magnitude of the gravitational force between a particle of mass m1 and one of mass m2 is given by F(x) = G m1m2 / x2, where G is a constant and x is the distance between the particles. (Use any variable or symbol stated above as necessary.) (a) What is the corresponding potential energy function U(x)? Assume that U(x) → 0 as x → [infinity]. U(x) =
The corresponding potential energy function U(x) = -Gm1m2/x, where G is the gravitational constant.
The potential energy function corresponding to the given gravitational force function is represented by the equation U(x) = -Gm1m2/x, where G is the gravitational constant.
To find the potential energy function, we need to integrate the force function with respect to the distance x.
This integration results in the negative sign and the inverse relation in the potential energy function.
The property that U(x) approaches 0 as x approaches infinity means that the potential energy becomes negligible at large distances, which is consistent with the behavior of gravitational potential energy.
Which region of the early universe was most likely to become a galaxy?
Answer:
This is likely possible for a region whose matter density is higher than the normal average.
Explanation:
A galaxy is a collection of lumps in space which are clumped together and interact with each other. There are a lot of speculations on how galaxies were birthed. some believe its formed by a collection of massive gas, dust which eventually collapsed under their own gravitational pull. others says its formed by the combination of large lumps of matter which accumulated forming thee galaxies. The possibility of a galaxy forming is dependent on how massive the matter in the region of the universe is.
High density regions in the early universe, referred to as colder spots, eventually evolved into galaxies. The process began with the creation of small galaxies and star clusters followed by massive star formation due to galaxy-galaxy collisions. Over time, the universe developed into the structure we see today.
Regions in the early universe that had higher-than-average density were most likely to become galaxies.
These regions attracted additional matter due to their higher density, and were sometimes referred to as the darkest or 'colder' spots of the early universe.
These colder spots of high density matter were where small galaxies and large star clusters first formed.
In these high density regions: the creation of small galaxies and large star clusters began when the universe was about two percent of its current age.
Galaxy-galaxy collisions in these regions erupted into massive bursts of star formation, some of which led to the formation of black holes.
Over time, clusters and superclusters of galaxies emerged and the universe began to resemble what we see today.
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Two gears are connected. Gear A has 10 teeth, while gear b has 40 teeth. If gear B turns at 10 rpms, how fast will gear a turn?
Answer:
w₁ = 40 rpm
Explanation:
Number of teeth of gear A = 10
Number of teeth of gear B = 40
Speed of gear B = w₂ = 10 rpm
Speed of gear A = w₁ = ?
Gear ratio is given by:
N₁/N₂ = w₂ / w₁
w₁ = N₂/N₁ * w₂
⇒ w₁ = 40/10 * 10
⇒ w₁ = 40 rpm
Gear A will turn at 40 rpms.
Explanation:In this scenario, we can use the formula for calculating the speed of rotation of gears. The formula is based on the principle that the number of teeth on a gear is inversely proportional to its speed. In other words, the smaller the gear, the faster it rotates.
Using the formula, we can calculate the speed at which gear A turns:
Speed of gear A = (Number of teeth on gear B/Number of teeth on gear A) x Speed of gear B
Plugging in the values, we get:
Speed of gear A = (40/10) x 10 = 40 rpms
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For trapezoid JKLM, A and B are midpoints of the legs. Find AB.
Question 3 options:
29
20
59
58
Answer:
AB = 29
Explanation:
For a better understanding, we must work this problem in a graphic way. In the attached image we can see the solution.
First, we draw a vertical dotted lines from the point J & K to the line ML, then we can see two new portions with the same length. Then with this simple analysis:
2x = 39 - 19
x = 10
Then we know that x = 10, another important data to find the answer is that the AB line is located in the midpoints of the legs. We also can see the right triangle MJ and the dotted line.
Now for every single right triangle, no matter its size and relationship between the vertical and the horizontal lengths, if some point is located in the hypotenuse (leg) at the middle of its length. This will be proportional to the vertical and the horizontal cathetus, therefore we will have the middle point on those two lines.
So, the AB line will be the sum of JK plus two times 5
AB = 19 + 5 + 5 = 29
Your pet hamster sits on a record player whose angular speed is constant. If he moves to a point twice as far from the center, then his linear speed
A) doubles.
B) halves.
C) remains the same.
Answer:
option A
Explanation:
given,
angular speed is constant
initial distance = r
final distance (r')= 2 r
initial linear velocity = v
final linear velocity = v'
we know,
v = r ω......................(1)
where r is the distance
ω is the angular speed
now,
v' = r' ω
v' = 2 r ω
v' = 2 v
hence, the linear velocity doubles.
The correct answer is option A
A stationary receiver detects a change in frequency of the signal from a jet flying directly away from it at 300 m/s. Which of the following receivers will detect the same change in frequency from a jet moving away at 600 m/s?A) A receiver moving at 900 m/s in the opposite direction as the jetB) A receiver moving at 300 m/s in the opposite direction as the jetC) A stationary receiverD) A receiver moving at 300 m/s in the same direction as the jet
Answer:
d) the receiver should be moving at 300 m/s in the same direction as the jet.
Explanation:
The change in the frequency of a moving sound (or wave) source is called Doppler Effect. The change in frequency is:
[tex]\Delta f=\frac{\Delta v}{v}f_{o}[/tex] (1)
with [tex]\Delta v=\mid v_{r}-v_{s}\mid[/tex] the velocity of the receptor respect the source, [tex] f_{o} [/tex] the real frequency and [tex] v [/tex] the velocity of the waves in the medium, we should be verty careful because the direction of the velocities are important so we have to select a reference frame and take on account the sign of the velocities. We're going to select positive direction as airplane direction. If we assume the frequency of the airplane sound and the velocity of waves on air remain constant, we should find the option that give us [tex] \Delta v=\mid v_{r}-v_{s}\mid = 300 [/tex] as the stationary case; let's see for:
a) [tex] \Delta v=\mid v_{r}-v_{s}\mid =\mid -900-600 \mid= 1500[/tex]
b) [tex]\Delta v=\mid v_{r}-v_{s}\mid = \mid-300-600 \mid= 900 [/tex]
c) [tex]\Delta v=\mid v_{r}-v_{s}\mid = \mid0-600\mid = 600 [/tex]
d) [tex]\Delta v=\mid v_{r}-v_{s}\mid= \mid300-600\mid = 300 [/tex]
So, the correct answer is d)
If the force of gravity suddenly stopped acting on the planets, they would
A. spiral slowly towards the sun.
B. continue to orbit the sun.
C. continue moving straight in the direction they are traveling.
D. spiral slowly away from the sun.
E. fly straight away from the sun.
Answer:c
Explanation:
If the Force of gravity suddenly stops acting on Planets then Planets would continue to move straight in the initial direction.
Gravity constantly acts on Planets to change their trajectory each instant thus in absence of it if a planet is moving in a circular path then it would follow the path of the tangent to the circular path as gravity force is absent to change its trajectory.
Answer:
c
Explanation:
because there would be no force directing the planet in any other direction
Suppose a piece of food is on the edge of a rotating microwave oven plate. Does it experience nonzero tangential acceleration, centripetal acceleration, or both when: (a) The plate starts to spin? (b) The plate rotates at constant angular velocity? (c) The plate slows to a halt?
Answer:
Explanation:
(a) When the plate starts to spin:
Its angular velocity increases, so the angular acceleration is non zero. As the direction of velocity keeps on changing every instant so the linear acceleration is also non zero.
(b) When the plate rotates at constant angular velocity:
Its angular velocity is constant so the angular acceleration is zero. As the direction of velocity keeps on changing every instant so the linear acceleration is also non zero.
(c) When the plate sows to halt:
Its angular velocity decreases, so the angular acceleration is non zero( but negative). As the direction of velocity keeps on changing every instant so the linear acceleration is also non zero.
A sled of mass m is coasting on the icy surface of a frozen river. While it is passing under a bridge, a package of equal mass m is dropped straight down and lands on the sled (without causing any damage). The sled plus the added load then continue along the original line of motion. How does the kinetic energy of the (sled + load) compare with the original kinetic energy of the sled? A) It is 1/4 the original kinetic energy of the sled. B) It is 1/2 the original kinetic energy of the sled. C) It is 3/4 the original kinetic energy of the sled. D) It is the same as the original kinetic energy of the sled. E) It is twice the original kinetic energy of the sled.
Answer:B
Explanation:
Given
mass of Sled is m
another package of mass m is thrown on it
Suppose u be the initial velocity of sled
conserving momentum
[tex]mu=2mv[/tex]
[tex]v=\frac{u}{2}[/tex]
where v is the final velocity
Initial kinetic energy [tex]=\frac{1}{2}mu^2[/tex]
Final Kinetic Energy[tex]=\frac{1}{2}(2m)\cdot (\frac{u}{2})^2[/tex]
Final Kinetic Energy[tex]=\frac{1}{2}\times \frac{1}{2}mu^2 [/tex]
Final kinetic Energy is half of initial
Measurements of how orbital speeds depend on distance from the center of our galaxy tell us that stars in the outskirts of the galaxy. True or False
Answer:
True
Explanation:
Measurements of how orbital speeds depend on distance from the center of our galaxy tell us that stars in the outskirts of the galaxy. True or False
stars in the outskirt orbit the galactic center
the object mean orbital speed depends only on the Earth's mass and the semi-major axis (half the longest diameter) of the object's orbit. worthy of note. the orbital speed changes depending on where in the orbit the object is. It will be greatest when closest to Earth and least when furthest from Earth.
A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating turntable. The effect of the weights is to double the rotational inertia of the system. As he is rotating, the man opens his hands and drops the two weights. They fall outside the turntable. Then:
A. his angular velocity doublesB. his angular velocity remains about the sameC. his angular velocity is halvedD. the direction of his angular momentum vector changesE. his rotational kinetic energy increases
Answer:
Explanation:CE
Let after the fall of weight from hands , the moment of inertia reduces from 2I to I. Since no external torque is acting on the system , angular momentum will be conserved.
I₁ ω₁ = I₂ ω₂
2I ω₁ = I ω₂
2ω₁ = ω₂
So , angular velocity will be doubled.
Option A is correct.
On a spending spree in Malaysia, you buy an ox with a weight of 28.9 piculs in the local unit of weights: 1 picul = 100 gins, 1 gin = 16 tahils, 1 tahil = 10 chees, and 1 chee = 10 hoons. The weight of 1 hoon corresponds to a mass of 0.3779 g. When you arrange to ship the ox home to your astonished family, how much mass in kilograms must you declare on the shipping manifest? (Hint: Set up multiple chain-link conversions.)
Answer:
1747.41 kg
Explanation:
If 1 piculs = 100 gins,
Then 28.9 piculs = (28.9 × 100) gins = 2890 gins.
Also,
If 1 gin = 16 tahils
then 2890 gins =( 16 × 2890 ) = 46240 tahils
Also,
If 1 tahil = 10 chees,
Then 46240 tahils = 46240 × 10 chees = 462400 chees.
Also,
If 1 chee = 10 hoons
Then 462400 chees =( 10 × 462400) hoons = 4624000 hoons.
Also,
If 1 hoon = 0.3779 g,
Then 4624000 hoons = 0.3779 × 4624000 = 1747409.6 g.
The mass in kg that i will declare in the shipping manifest = (1747409.6/100 )kg = 1747.41 kg
If you are going 30 miles an hour in good condition, it will take how many feet to stop .
Answer:
158400 feet per hour
Explanation:
First we find:
How many feet are in miles per hour?
Multiply your speed in miles per hour by 5,280. This is the number of feet in a mile. The result is your speed in feet per hour.
For example, 30 miles per hour times 5,280 feet per mile is 158,400 feet per hour.
Kelli weighs 425 N, and she is sitting on a playground swing that hangs 0.36 m above the ground. Her mom pulls the swing back and releases it when the seat is 1.00 m above the ground. Assume that air resistance is negligible. (a) How fast is Kelli moving when the swing passes through its lowest position?
Answer:
V = 3.54 m/s
Explanation:
Using the conservation of energy:
[tex]E_i = E_f[/tex]
so:
[tex]wh = \frac{1}{2}mV^2[/tex]
where w is te weigh of kelly, h the distance that kelly decends, m is the mass of kelly and V the velocity in the lowest position.
So, the mass of kelly is:
m = 425N/9.8 = 43.36 Kg
and h is:
h = 1m-0.36m =0.64m
then, replacing values, we get:
[tex](425N)(0.64m) = \frac{1}{2}(43.36kg)v^2[/tex]
Solving for v:
V = 3.54 m/s
Two skaters skate toward each other, each moving at 3.3 m/s. Their lines of motion are separated by a perpendicular distance of 1.5 m. Just as they pass each other (still 1.5 m apart), they link hands and spin about their common center of mass. What is the rotational speed of the couple about the center of mass? Treat each skater as a point particle, each with an inertia of 51 kg.
Answer:
4.4 rad/s
Explanation:
When the 2 skaters is spinning with a distance of 1.5m, their rotation radius is half of that distance, which is 1.5/2 = 0.75m.
Then their moments of inertia, given that their mass being 51 kg, is (treating them as point mass particle):
[tex]I = Mr^2 = 2Mr^2 = 51*0.75^2 = 38.25 kg.m^2[/tex]
When they change from linear motion to rotational motion, their energy must be conserved:
[tex]E_L = E_r[/tex]
[tex]2*(0.5Mv^2) = 2*(0.5I\omega^2)[/tex]
[tex]\omega^2 = \frac{Mv^2}{I}[/tex]
[tex]\omega = v\sqrt{\frac{M}{I}}[/tex]
[tex]\omega = 3.3\sqrt{\frac{51}{38.25}} = 4.4 rad/s[/tex]
The rotational speed of the couple about the center of mass is: 4.4 rad/s
Meaning of CoupleA couple can be defined as an effect or force created by two parallel forces that are equal in masses but opposite in sense or opposite in direction and do not share the same line of action.
The couple can also be used to signify two individuals.
In conclusion, the rotational speed of the couple about the center of mass is: 4.4 rad/s
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The percentage of incident light radiation reflected back to space is termed albedo. True or false?
Answer:True
Explanation:
Albedo is a unit-less, non-dimensional quantity that shows how well a surface reflects solar energy. The value of albedo can vary from 0 to 1, 0 being the black and 1 refers to a white surface. Zero means Surface is a perfect absorber i.e. it absorbs all the incoming rays incidents on it. Albedo 1 means the surface is a perfect reflector.
Albedo usually applies for visible light, even though it may involve some of the infrared regions of the electromagnetic spectrum. The average albedo associated with earth surface is 30%
A) True. The percentage of incident light radiation reflected back to space is termed albedo.
Definition of Albedo: Albedo is a measure of the reflectivity of a surface. It is defined as the fraction or percentage of incoming solar radiation that is reflected back into space by a surface.
Surfaces and Albedo: Different surfaces have varying albedos. Light-colored surfaces, such as snow and clouds, have high albedos and reflect more sunlight, while dark surfaces, such as forests or oceans, have low albedos and absorb more sunlight.
Earth's Albedo: On average, Earth's albedo is approximately 30%, which means that about 30% of the solar radiation that reaches Earth is reflected back into space. This plays a significant role in the Earth's radiation budget and climate.
Why it Matters: The albedo effect is crucial in understanding climate dynamics because it influences how much solar energy is absorbed by the Earth's surface and, consequently, impacts global temperatures.
Which aspect of the scientific method occurs first?
a. hypothesis
b. data collection
c. experiment
d. observation
Answer:
The right option is d. observation
Explanation:
Observation: These is the state of being very alert about the what is happening around. Observation in science can be done using the sense organs such eyes to spot out differences, nose to smell the release of gases, ears to hear sound, skin to feel changes in temperature. Observation is the first scientific method. And it can be carried out anywhere.
Observation leads pattern, pattern leads to problems, problems leads to hypothesis, hypothesis leads to experiment, experiment leads to Theory.
Therefore the right option is d. observation
The correct answer is observation, which is in option d. In the scientific method, observation is the first step. It involves gathering information about a phenomenon or a specific aspect of the natural world through careful and systematic observation.
The process of observation allows scientists to identify patterns, make initial observations, and ask questions about the phenomenon they are studying. It serves as the foundation for scientific inquiry and guides the subsequent steps of the scientific method. After making observations, scientists then move on to formulating a hypothesis, which is a proposed explanation or prediction based on the observed data. The hypothesis is a tentative answer to the research question and serves as the starting point for further investigation.
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A ball is thrown up into the air with an initial velocity of 64 ft/sec. The ball is 4 ft above the ground when it is released. Its height, in feet, at time t seconds is given by: h(t) = −16t^2 + 64t + 4. What is the time when it reaches its maximum height?
Answer:
2 seconds and maximum height reached is 68 ft
Explanation:
h (t) = -16t^2 +64t +4
differentiate with respect to t
h'(t) = -32t +64
for maximum height velocity which is h'(t) must be zero
-32t +64 = 0
-32t = -64
t = 2 s
hence height is
h(2) = -16(2)^2 +64(2) +4
h(2) = -64+128+4
h(2) = 68 feet
If water is leaking from a certain tank at a constant rate of 1,200 milliliters per hour, how many seconds does it take for 1 milliliter of water to leak from the tank?
Answer:
It will take 3 seconds for 1 milliliters of water to leak from the tank.
Explanation:
The rate of leak = volume of water/Time
Q = V/t .................................. equation 1
making t the subject of the equation above,
t = V/Q............................. Equation 2.
where Q = rate of leak, V = volume of water, t = time
Given: Q = 1200 milliliters per hour, V = 1 milliliters.
Substituting these values into equation 2
t = 1/1200
t = 0.00083 hours.
If I hours = 3600 seconds,
Then, 0.00083 hours = 0.00083×3600 seconds
= 3 second.
Therefore it will take 3 seconds for 1 milliliters of water to leak from the tank.
If cells are placed in a hypertonic solution containing a solute to which the membrane is impermeable what could happena)cells would shrink then later reach equilibriumb)cell swell and ultimately burstc)cell show no changed)loose water and shrink
Answer:
cell swell and burst(b)
Explanation:
This process is called hemolysis. it also occurs in a red blood cell.
In a conversation with a friend, he expresses skepticism about global warning. When you inquire about his reasons, he responds by saying that the weather in that area has been the coolest he can remember. Using the information you have learned, what information could you offer to encourage your friend to reevaluate his position?
Answer:
Explanation:
A friend observes only the weather which is different than climate. Weather refers to short term change in the atmosphere while climate refers to what weather is like over a while in a specific area.
The weather may change when we move from one area to another. Cooler weather does not mean that the climate is cooler.
Global warming is the increase in average temperature globally due to which heat is increasing but it does not imply that temperature is hotter everywhere.
If an alpha particle and a beta particle have the same energy, which particle will penetrate farther into an object?
Answer:
Beta particle
Explanation:
If an alpha particle and a beta particle have the same energy, beta particle will penetrate farther into an object than alpha particle because;
1. In air, beta particles can travel a few hundred times farther than alpha particles.
2. Beta particles have more penetrating power than alpha particles.
3. Alpha particle can be absorbed or stopped by an inch or less 1-2 centimeters of air or a thin piece of tissue while beta particles can be stopped or absorbed by a thin layer of Aluminium.
4. Alpha particles loose all of their energies in a small volume easily that beta particles.
5. Beta particles can traveled a longer distance between 2-3 meters at a speed nearly equal to that of light than alpha particles which travel a distance between 2-4 cm at a speed approximately five percent the speed of light.
A 296-kg motorcycle is accelerating up along a ramp that is inclined 26.2° above the horizontal. The propulsion force pushing the motorcycle up the ramp is 3106 N, and air resistance produces a force of 286 N that opposes the motion. Find the magnitude of the motorcycle's acceleration.
Answer:
The magnitude of the motorcycle's acceleration is 5.20 m/s².
Explanation:
Given that,
Mass of motorcycle = 296 kg
Angle = 26.2°
Force on motorcycle= 3106 N
Force = 286 N
We need to calculate the magnitude of the motorcycle's acceleration
The net force acting on the motorcycle
Using newton's second law
[tex]ma=F_{p}-F_{air}-F_{g}[/tex]
[tex]ma=F_{p}-F_{air}-mg\sin\theta[/tex]
Put the value into the formula
[tex]296a=3106-286-296\times9.8\times\sin26.2[/tex]
[tex]a=\dfrac{3106-286-296\times9.8\times\sin26.2}{296}[/tex]
[tex]a=5.20\ m/s^2[/tex]
Hence, The magnitude of the motorcycle's acceleration is 5.20 m/s².