The given question requires calculating the work done to pump liquid into a specifically shaped container by integrating the weight of the liquid over the height it is lifted, taking gravity into account.
Explanation:The question concerns calculating the work required to pump liquid into a container. This container has been formed by revolving the region bounded by y=x^2 and the x-axis around the y-axis, between x=0 and x=2. When calculating the work done in a physics context, the scenario typically involves considerations of force, distance, and energy. For this particular case, you would use the concept of work done against gravity to fill the container with a liquid from a source below its base, which involves integrating the weight of the liquid elements being moved over the height they are lifted. The fact that pg=1 implies we're assuming a uniform density of the liquid and a gravitational field strength of 1, probably to simplify calculations. However, without additional information such as vector force fields or specific motion paths like in other provided excerpts, we can't calculate an exact numerical answer here.
A block of mass 3.3 kg, sliding on a horizontal
plane, is released with a velocity of 1.8 m/s.
The blocks slides and stops at a distance of
1.5 m beyond the point where it was released.
How far would the block have slid if its
initial velocity were quadrupled?
Answer:
24 m
Explanation:
initial velocity is u = 3.5 m/sec
final velocity is v = 0 m/sec
distance traveled is S = 1.5 m
From kinematic equation [tex]v^{2}-u^{2} = 2as[/tex]
Making acceleration the subject,
[tex]a=\frac {v^{2}-u^{2}}{2s}[/tex]
Acceleration [tex]a = \frac {0^2-3.5^2}{(2*1.5)}= -4.083333333m/s^{2}[/tex]
When the initial velocity is quadrupled= u = 3.5*4 = 14 m/s
V = 0 m/s
[tex]a = -4.083333333m/s^{2}[/tex]
then [tex]S = \frac {v^{2}-u^{2}}{2} = \frac {0^{2}-14^{2}}{2\times -4.083333333} = 24 m[/tex]
please help with this assignment paper in science.
I gotta get it done before Monday.
thx.
Explanation:
(a) The net force in the y direction is the sum of the individual forces. Taking up to be +y:
∑F = Lift − Weight
∑F = 100,000 N − 75,000 N
∑F = 25,000 N
(b) Since the net force is not 0, the forces are unbalanced.
(c) Since the lift is greater than the weight, the plane will rise.
(d) The net force in the x direction is the sum of the individual forces. Taking forward to be +x:
∑F = Thrust − Drag
∑F = 200,000 N − 23,000 N
∑F = 177,000 N
(e) Since the net force is not 0, the forces are unbalanced.
(f) Since the thrust is greater than the drag, the plane will accelerate.
16. A 7500 kg 18-wheeler traveling at 20 m/s exits onto the runaway truck ramp on the freeway.
When it comes to a stop, it is 10 m higher than before.
How much energy was dissipated by friction?
Answer:
765,000 Joule
Explanation:
Principle of Conservation of Energy
The total energy in an isolated system cannot be created or destroyed, but transformed. Moving objects have kinetic energy, objects placed in some height above a reference level have gravitational potential energy. When they change their motion variables, one energy converts into the other, but if the numbers don't fit, we know there was some other type of energy acting into the system. The most common reason for energy 'losses' is the thermal energy, produced when objects move in rough surfaces or take friction from the air.
The 7,500 kg truck is originally traveling at 20 m/s to a certain height we'll set to 0. Thus, its total energy is
[tex]\displaystyle E_1=\frac{mv^2}{2}[/tex]
[tex]\displaystyle E_1=\frac{7,500\ 20^2}{2}[/tex]
[tex]E_1=1,500,000\ Joule[/tex]
When it comes to a stop, its speed is 0 and its height is 10 m higher than before. It means all the kinetic energy was transformed into other types of energy. The gravitational potential energy is
[tex]U=mgh=(7,500)(9.8)(10)=735,000\ Joule[/tex]
Since this number is not equal to the previous value of the energy, the difference is due to thermal energy dissipated by friction
[tex]E_t=1,500,000\ Joule-735,000\ Joule=765,000\ Joule[/tex]
why do we increase potential difference along power lines
Answer:
The primary reason that power is transmitted at high voltages is to increase efficiency. As electricity is transmitted over long distances, there are inherent energy losses along the way. ... The higher the voltage, the lower the current. The lower the current, the lower the resistance losses in the conductors.
Explanation:
How does pressure affect surface tension
the effect of pressure on surface tension can be attributed in part to absorption of gas at the surface of the liquid and in part to an intrinsic decrease in density of the liquid in the neighborhood of the surface.
In the case of liquids , Owing to contact forces between the edge of the surface and the vessel, the surface acquires a curvature, and if the liquid rises up at the edges where it meets the vessel, the pressure will be less in the liquid than in the air, for points just below and just above the surface. The vessel exerts an upward force on the liquid. This is simply a matter of looking at the directions of forces acting, knowing that the surface is under tension.
What is the velocity of the ball 0.8 seconds after it’s released ?
Need more details, what is the slope of the line, etc.
It depends.
In order to answer the question, a person has to know:
-- the velocity (speed and direction) of the ball WHEN it's released
-- whether the ball has any net electric charge
-- whether there's any other net electric charge in the neighborhood
-- the mass of the ball, if any net charges are involved
-- what planet is nearest to the ball
-- the acceleration of gravity on that planet
Each of these details has an influence on the answer. That is, if one of them changes, then the answer changes. Now, it hasn't escaped my notice that you neglected to provide ANY of this information, so there's no way to even begin to concoct an answer.
Right now, the question is a lot like me asking you "How much will I weigh 8 seconds after I finish eating the steak ?".
13. If you have 800 radioactive atoms, and they undergo
14 half-lives, how many will remain? Show your math.
There will be zero radioactive atoms left
Explanation:
The amount of radioactive atoms left of a radioactive sample after a certain time t is given by the equation
[tex]N(t) = N_0 (\frac{1}{2})^{-\frac{t}{\tau}}[/tex]
where
N(t) is the number of radioactive atoms left after time t
[tex]N_0[/tex] is the initial number of radioactive atoms
[tex]\tau[/tex] is the half-life of the sample
In this problem we have:
[tex]N_0 = 800[/tex] (initial number of radioactive atoms)
[tex]t=14 \tau[/tex] (we want to evaluate the number of atoms left after 14 half-lives)
Substituting, we find:
[tex]N(14\tau) = (800)(\frac{1}{2})^{-\frac{14\tau}{\tau}}=0.049[/tex]
This means that there will be zero atoms left, since atoms can't be split in fractional parts.
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An 800-N man stands at rest on two bathroom scales so that his weight is distributed evenly over both scales. The reading on each scale is
400 N
The weight of the man is evenly distributed on each scale
The man's total weight of 800-N, when distributed equally over two bathroom scales, will result in each scale reading 400-N.
Explanation:The man's total weight is 800-N and he is standing on two scales, with his weight distributed evenly. This means each scale will bear half of the total weight. Therefore, the reading on each scale will be 800-N divided by 2. That calculation yields a result of 400-N per scale. So each bathroom scale will show a weight of 400-N, assuming the weight distribution remains equals.
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A radar station sends out a 250000 Hz sound wave at a speed of 340 m/s. The sound wave bounces off a weather ballon and returns back to the radar station in 4.8s at a frequency of 240000 hz. How far away from the radar station is the ballon and what direction is it moving?
Answers:
a)The balloon is 68 m away of the radar station
b) The direction of the balloon is towards the radar station
Explanation:
We can solve this problem with the Doppler shift equation:
[tex]f'=\frac{V+V_{o}}{V-V_{s}} f[/tex] (1)
Where:
[tex]f=250,000 Hz[/tex] is the actual frequency of the sound wave
[tex]f'=240,000 Hz[/tex] is the "observed" frequency
[tex]V=340 m/s[/tex] is the velocity of sound
[tex]V_{o}=0 m/s[/tex] is the velocity of the observer, which is stationary
[tex]V_{s}[/tex] is the velocity of the source, which is the balloon
Isolating [tex]V_{s}[/tex]:
[tex]V_{s}=\frac{V(f'-f)}{f'}[/tex] (2)
[tex]V_{s}=\frac{340 m/s(240,000 Hz-250,000 Hz)}{240,000 Hz}[/tex] (3)
[tex]V_{s}=-14.16 m/s[/tex] (4) This is the velocity of the balloon, note the negative sign indicates the direction of motion of the balloon: It is moving towards the radar station.
Now that we have the velocity of the balloon (hence its speed, the positive value) and the time ([tex]t=4.8 s[/tex]) given as data, we can find the distance:
[tex]d=V_{s}t[/tex] (5)
[tex]d=(14.16 m/s)(4.8 s)[/tex] (6)
Finally:
[tex]d=68 m[/tex] (8) This is the distance of the balloon from the radar station
Two objects are identical except that one is hotter than the other.Compare how they respond to identical forces.
Answer:
Two objects are identical except that on is hotter than the other. Thus, when an equal force acts on them the hotter one will move faster or will get displaced more or stop slower than the other one. This is because the hotter object has comparatively more mobile particles than the other
Hope this helps!
Final answer:
Identical forces exerted on two objects with different temperatures will affect them equally according to Newton's third law, but their responses, such as stress and expansion, may differ due to properties like thermal expansion coefficients. Also, at thermal equilibrium, the final temperature is closer to the object with greater heat capacity. The hotter star of two identical stars will be significantly brighter.
Explanation:
Response to the Student's Question
When two objects are identical except for temperature and they are exposed to identical forces, the forces they experience will be the same due to Newton's third law. However, the effect of the force may differ if their temperatures lead to different physical properties like thermal expansion. If object A has a higher thermal expansion coefficient than object B and both are heated identically, A will likely feel greater stress because it will expand more, which could create internal strain if constrained. For the question about the heat capacities, when two objects—one hot, one cold—are brought into contact, the final temperature at thermal equilibrium will be closer to the object with the higher heat capacity, in this case, the colder object. Therefore, it will not be exactly halfway between the two initial temperatures.
In the context of stars, brightness is related to temperature. The star with a temperature of 8700 K will be brighter than the star at 2900 K due to Wien's Law and the Stefan-Boltzmann Law, which relate temperature to luminosity and energy output. The hotter star is, therefore, significantly brighter.
What does energy do, according to the conservation of energy? cannot be created, but it can be destroyed can be created, but it cannot be destroyed cannot be created or destroyed can be created and destroyed PLZ WILL MARK AS BRAINLIST
Answer:
Energy cannot be created or destroyed.
Explanation:
Energy cannot be created or destroyed, it can only be altered from one from to another.
Answer:
C. Energy cannot be created or destroyed but it can change form.
Energy can be converted from one form to another. The law of conservation of energy says that energy is neither created nor destroyed. When you consume energy, it is not gone forever. Instead, it is changed from one form of energy to another. So, energy is not manufactured and it doesn't go away after you use it. It is just transformed, or stored.
4.
A baseball player throws a baseball straight up into the air with an initial speed of 25 m/s.
A. What is the maximum height to which the ball rises?
B. What is the speed of the ball when it is halfway up to its maximum height?
A) The maximum height is 31.9 m
B) The speed of the ball is 17.7 m/s
Explanation:
A)
We can solve this problem by using the law of conservation of energy. In fact, in abcense of air resistance, the mechanical energy of the ball (sum of potential energy + kinetic energy) must be conserved.
Mathematically:
[tex]U_i +K_i = U_f + K_f[/tex]
where :
[tex]U_i[/tex] is the initial potential energy, at the bottom
[tex]K_i[/tex] is the initial kinetic energy, at the bottom
[tex]U_f[/tex] is the final potential energy, at the top
[tex]K_f[/tex] is the final kinetic energy, at the top
We can rewrite it as
[tex]mgh_i + \frac{1}{2}mu^2 = mgh_f + \frac{1}{2}mv^2[/tex]
where:
m is the mass of the ball
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
[tex]h_i = 0[/tex] is the initial height of the ball
u = 25 m/s is its initial speed
[tex]h_f[/tex] is the maximum height reached by the ball
v = 0 is the final speed (which is zero at the maximum height)
Solving for [tex]h_f[/tex], we find: the maximum height:
[tex]\frac{1}{2}mu^2 = mgh_f\\h_f = \frac{u^2}{2g}=\frac{(25)^2}{2(9.8)}=31.9 m[/tex]
B)
When the ball is halfway up to its maximum height, it means that its height is
[tex]h_f = \frac{31.9}{2}=15.9 m[/tex]
Therefore we can re-apply again the equation of the conservation of energy:
[tex]mgh_i + \frac{1}{2}mu^2 = mgh_f + \frac{1}{2}mv^2[/tex]
where this time v is not zero, but it is the speed of the ball at the height of 15.9 m
Re-arranging the equation and solving for v, we find:
[tex]v=\sqrt{u^2-2gh_f}=\sqrt{25^2-2(9.8)(15.9)}=17.7 m/s[/tex]
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The maximum height the baseball can reach when thrown at an initial speed of 25 m/s is 31.9 meters. When the ball is halfway to this height, its speed is 17.67 m/s.
Explanation:The subject matter of the question is physics, specifically the concepts of motion, velocity, and gravitational forces.
Given the initial velocity of the baseball is 25 m/s and the acceleration due to gravity is -9.8 m/s², we can find the maximum height using the equation v² = u² + 2gs, where v is the final velocity, u is the initial velocity, g is acceleration due to gravity, and s is displacement.
Substituting in the given values gives us 0 = (25 m/s)² + 2*(-9.8 m/s²)*s, so s = (25 m/s)² / (2 * 9.8 m/s²) = 31.9 meters. This is the maximum height the ball reaches.
When the ball is halfway to its maximum height, it is still subject to the laws of physics, so we cannot simply divide the initial velocity by two. Instead, we can find the velocity at the halfway height (15.95 meters) using the equation v = u + 2gs. Substituting the known values, we get v = sqrt((25 m/s)² + 2*(-9.8 m/s) * (-15.95 m) ) = 17.67 m/s.
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Point charge q1 of 30 nC is separated by 50 cm from point charge q2 of -45 nC. As shown in the diagram, point a is located 30 cm from q1 and 20 cm q2. What are the magnitude and direction of the electric field at point a? Let the electrostatic constant k= 8.99 x 10^9 N x m^2/C^2
Answer:
E1 = 2996.667N/C E2 = 11237.5N/C
Explanation:
E1 = kQ1/r^2
=8.99 x 10^9 x 30 x 10^-9/(30x10^-2)^2
= 2996.667N/C
E2 = kQ2/r^2
= 8.99 x 10^9 x 50 x 10^-9/(20x10^-2)^2
= 11237.5N/C
The direction are towards the point a
how is humidity related to air pressure
A.) air pressure is lower below sea level because of the humidity
B.) humid air is lighter, so it has lower pressure
C.) humidity and air pressure are not related
D.) humid air has higher pressure because of the heaviness of water
PLEASE HELP
Answer:
Humid air is lighter so it has lower pressure
Explanation:B.) humid air is lighter, so it has lower pressure
Explanation:
Humidity is related to air pressure in that, a humid air is lighter and it has very low pressure.
Air is heavier than water vapor.
The main component of humid air is water vapor.
Water vapor is mostly water in its gaseous form
We know that for a single mole of water, the mass is 18g
Air is a mixture of gases with Nitrogen gas dominating.
A mole of nitrogen gas has a mass of 28g.
We can see that air that is humid i.e contains more water vapor is lighter and it has a lower pressure.
Formulas (equations): A = 3x and B = 5x + 1
As x increases, does A or B go up faster?
if x=0, then A=?
if x=1 then B=?
Answer:
B goes up faster
if x=0, then A=0
if x=1 then B=6
Explanation:
Formulas Or Equations
We have two different formulas
A = 3x
B = 5x + 1.
They both are equations of lines. The number beside the X (coefficient) is also known as the slope of the line. The greater the slope, the faster the function goes up as X increases. We can clearly see that the equation B has a greater slope, which means it goes up faster than A as X increases
When x=0, A=3(0)=0
When x=1, B=5(1)+1=6
Beth exerts 14 N force to propel a 4.5 kg bowling ball down the lane
Answer:
It will have a certain kinetic energy at the beginning, but it will be lost by resistant work done by friction. Thus, itsmotion wil be uniformly decelerating.
Explanation:
A ball is projected horizontally from a table 1.0 m high and hits the ground after falling from a time t=0.45s. If the ball travels horizontally a distance x = 3.0 m in that time it’s initial velocity was equal to
The initial velocity is [tex]6.7 m/s[/tex]
Explanation:
The motion of the ball is a projectile motion, therefore it consists of two independent motions:
- A uniform motion (constant velocity) along the horizontal direction
- A uniformly accelerated motion, with constant acceleration (acceleration of gravity) in the downward direction
In this problem, we just need to analyze the horizontal motion: the horizontal velocity is constant, therefore the horizontal distance travelled is given by
[tex]x=v_x t[/tex]
where
[tex]v_x[/tex] is the horizontal velocity
t is the time of flight
Here we have:
t = 0.45 s
x = 3.0 m
And so solving for [tex]v_x[/tex], we find
[tex]v_x = \frac{3.0}{0.45}=6.7 m/s[/tex]
And since the ball was initially projected horizontally, this is also the initial velocity.
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The initial velocity of the ball is 6.67 m/s.
Explanation:To determine the initial velocity of the ball, we need to use the horizontal motion equation, which states that the horizontal distance traveled equals the product of the initial velocity and the time of flight. In this case, the horizontal distance traveled is 3.0 m and the time of flight is 0.45 s. Rearranging the equation, we find that the initial velocity is equal to the horizontal distance divided by the time of flight.
Initial velocity = horizontal distance / time of flight = 3.0 m / 0.45 s = 6.67 m/s
Therefore, the initial velocity of the ball is 6.67 m/s.
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1. A container has a mass of 36 kg. How much does the container weigh?
Answer:
352.8 N
Explanation:
= 36
= 9.8
⁄ = ? = = 36 × 9.8 = 352.8
Answer:
360 N
Explanation:
mass = 36 kg
g = 10m/s²
W = mg
W = 36 × 10
W = 360 N
Maria does 500 Newton-meters of work moving books from one table to another. The total force is 100 Newtons. How far were the books moved?
The displacement of the book is 5 meters
Explanation:
The work done by a force when moving an object is given by:
[tex]W=Fd cos \theta[/tex]
where :
F is the magnitude of the force
d is the displacement
[tex]\theta[/tex] is the angle between the direction of the force and the displacement
In this problem, we have:
W = 500 J is the work done by Maria
F = 100 N is the force applied by Maria
[tex]\theta=0^{\circ}[/tex], assuming the direction of the force is parallel to the displacement
So we can rearrange the equation to solve for d, the displacement:
[tex]d=\frac{W}{F cos \theta}=\frac{500}{(100)(cos 0)}=5 m[/tex]
So, the book was moved 5 meters.
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Does anyone know about this : Applying the Parallelogram of Forces Law. Or does anyone know of any notes about that???
Answer:
Explanation:
The force is a vector magnitude, it has direction, course and intensity.
Suppose that you have given two forces at a certain angle and that you need to find the resultant force then you apply the Parallelogram of force low.
You represent the two forces in the drawing as vectors and connect their origin to the same point and then construct a parallelogram over them.
The longer diagonal represents the resultant force.
God is with you!!!
What characteristics of water waves make them transverse waves?
Answer:
The characteristics of water waves is that it travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases.
Explanation:
What is an independent variable?
The variable that is kept the same in the experiment.
The variable that the scientist change
The result of the experiment.
The data within the experimen
Answer:
variable that scientist change
Explanation:
Greg is in a bike race. At mile marker four (out of ten), his speed was measured at 13.5 mph.
Which best describes the measured number?
It is the average speed of the bike rider.
It is the instantaneous speed of the bike rider.
It is the instantaneous velocity of the bike rider.
It is the average velocity of the bike rider.
Answer:
B: it is the instantaneous speed of the bike rider.
Explanation:
keep it going....
Answer:
B It is the instantaneous speed of the bike rider.
Explanation:
I took the test
what does voltage describe
Answer:
Voltage describes the potential difference between the two ends of a conductor and thus , more the voltage , more will be the flow of current through the conductor ( more no of electrons and faster speed).
Explanation:
Voltage represents the potential difference between two ends of a conductor, and so the greater the voltage, the greater the current flow through the wire.
What is ohm’s law?Ohm's law claims that the voltage across a conductor is directly proportional to the current flowing through it.
Ohm's law claims that the voltage across a conductor is directly proportional to the current flowing through it.
This current-voltage connection may be expressed mathematically as,
The Equation of Ohm's Law
V=IR
Voltage represents the potential difference between two ends of a conductor, and so the greater the voltage, the greater the current flow through the wire.
Hence, Voltage is described as the product of the current and the resistance.
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A ball of mass 100g falls from a height of 3m on to a horizontal surface and rebounds to a height of 2m. calculate the change in momentum and the kinetic energy of the ball it strikes the surface
The change in momentum is equal to 1.3928 kg.m/s².
The kinetic energy of the ball as it strikes the surface = 2.94 Joules
Explanation:Given:
Mass of the ball = 100 g = 100 × 10⁻³ kg = m = 0.1 kg
Height from which ball falls = h = 3 m
Height to which the ball rebounds = h' = 2 m
g= acceleration due to gravity = g = 9.8 m/s²
1. A ball dropped from a height of 3 m, hits the horizontal surface and bounces back. This will cause a change in momentum.
The velocity of the ball before hitting the surface and after hitting the surface is different; causing a change in momentum (Δp).
Since momentum (p) = mass (m) × velocity (v) : [tex]p=m\times v[/tex]
Δp = [tex]m\times V_\ after[/tex] [tex]-\ m\times V_\ before[/tex] = [tex]m\times (V_\ after[/tex] [tex]\ -\ V_\ before[/tex] [tex])[/tex] ...........................(1)
Velocity (v) is given by [tex]v = \sqrt{2gh}[/tex]
[tex]V_\ before[/tex] = [tex]\sqrt{2\times g\times h} = \sqrt{2\times 9.8\times 3} = \sqrt{58.8} = 7.668\ m/s^2[/tex]
[tex]V_\ after[/tex] = [tex]\sqrt{2\times g\times h'} = \sqrt{2\times 9.8\times 2} = \sqrt{39.2} = 6.2609\ m/s^2[/tex]
[tex]V_\ before[/tex] is a decreasing quantity (Ball dropped from 3 m) until it becomes equal to [tex]V_\ after[/tex] and hence is a negative vector (negative in sign and opposite in direction to [tex]V_\ after[/tex].)
[tex]V_\ before[/tex] = (-7.668 m/s²)
From (1), for m = 0.1 kg, Δp becomes;
Δp = [tex]m\times (V_\ after[/tex][tex]\ -\ V_\ before[/tex][tex])[/tex] = [tex]0.1( 6.2609 - ( - 7.668)) = 0.1\times 13.9289 = 1.3928\ kg.m/s[/tex]
2. As a ball falls to the surface, its gravitational potential energy is transformed into kinetic energy. This kinetic energy keeps on increasing with increase in momentum until it strikes the surface.
K.E of ball just before it strikes the surface from 3 m height = [tex]K.E = mgh[/tex]
[tex]K.E = 0.1\times 9.8\times 3 = 2.94\ J[/tex]
What is the name for a diagram like this one?
Phytoplankton > Shrimp > Salmon > People
A.) An aquatic habitat
B.) A latitude
C.) A niche
D.) A food chain
Answer:
food chain
Explanation:
The given flow chart or diagram represents a food chain . A food chain is the flow of energy from lower level organism to higher level organism.
What is food chain?In ecology, the food chain is the flow of substance and energy from one organism to another in the form of food. Due to the fact that most species consume more than one kind of animal or plant, food chains locally entangle to form a food web.
The main source of food are plants since they use photosynthesis to turn solar energy into food.A flesh-eating animal consumes a plant-eating species in a predator chain. A smaller organism in a parasite chain takes a portion of a larger host and may also become a parasite on itself.
Here, the phytoplanktons are eaten by shrimps and they are in turen eaten by salmon which is edible to humans. Hence, the diagram represents a food chain.
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A skydiver jumped out of a plane, determine distance he distance he descended after 5 seconds. Gravity is pulling him down at 10 m/s^2
The distance travelled in 5 seconds is 125 m
Explanation:
The motion of the skydiver is a free fall motion, since he is acted upon the force of gravity only. Therefore, it is a uniformly accelerated motion, with constant acceleration downward, and we can find the distance he travels by using the following suvat equation:
[tex]s=ut+\frac{1}{2}at^2[/tex]
where
s is the distance travelled
u is the initial velocity
t is the time
a is the acceleration
In this problem, we have:
u = 0 (the skydiver jumps from rest)
[tex]a=g=10 m/s^2[/tex] (acceleration of gravity)
And substituting
t = 5.0 s
we find the distance travelled:
[tex]s=0+\frac{1}{2}(10)(5)^2=125 m[/tex]
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1.
A person throws a shot put from height of 5 feet with an initial vertical
velocity of 40 feet per second. Use the vertical motion model,
h = -16ť+ vt +s, where v is the initial velocity in feet per
second and s is the initial height in feet, to calculate the amount of
time the shot put is in the air before it hits the ground. Round your
answer to the nearest tenth if necessary.
Time in air:
seconds
The amount of time the shot-put spent in the air before it hits the ground is 3 sec
given the data in the question;
A person throws a shot-put from height, initial height; s = 5ft
Initial vertical velocity or speed; v = 40 ft/s
Now, it is said that, vertical motion model is;
[tex]h = -16t^2 +vt + s[/tex]
so we substitute in the given values
[tex]h = -16t^2 + (40ft/s * t) + 5ft[/tex] --------------Let this be equation 1
To calculate the amount of time the shot-put spent in the air before it hits the ground.
We say: height; h = 0 i.e when the shot-put touches the ground, the height becomes zero.
so we substitute in h=0 in equation 1
[tex]0 = -16t^2 + (40ft/s * t) + 5ft[/tex]
we rearrange
[tex]16t^2 - 40t - 5 = 0[/tex]
To solve for "t", we use the quadratic equation
[tex]x = \frac{-b\±\sqrt{b^2-4ac} }{2a} \\[/tex]
as [tex]ax^2 +bx-c = 0[/tex], we take each value from its position and substitute into the quadratic equation
so
a = 16
b = -40
c = -5
so substitute
[tex]x = \frac{-(-40)\±\sqrt{(-40)^2 - (4*16*(-5)} }{2*16} \\\\x = \frac{40\±\sqrt{1600+320} }{32}[/tex]
[tex]x = \frac{40\±\sqrt{1920} }{32}\\so\\\\x = \frac{40+\sqrt{1920} }{32} or \frac{40-\sqrt{1920} }{32} \\\\x = 2.62\\or\\ x = -0.12\\[/tex]
we know that, time can not be negative,
Hence x = 2.62 ≈ 3 sec { nearest tenth }
Therefore, the amount of time the shot-put spent in the air before it hits the ground is 3 sec
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Why are politics and political science important?
Politics is important as it governs decision making within societies and manages conflict, while political science provides an understanding of these processes and systems, enabling informed citizenship.
Explanation:Politics and political science are important for several reasons. Firstly, politics is how societies make collective decisions. It determines the distribution of power, resources, and responsibilities within a society. Additionally, politics also manages conflict and ensures social order. Secondly, political science is the systematic study of politics and government. It equips individuals with the knowledge and analytical skills to understand political behavior and policymaking processes, which is essential for informed citizenship.
Through political science, we can understand how different political systems work, compare them, and analyze their impacts on their constituents. Whether intending to participate directly in politics or just wanting to be a well-informed citizen, understanding politics and political science is integral.
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Final answer:
Politics and political science are crucial as they determine resource allocation and decision-making within societies. Understanding and participating in politics can shift power toward ordinary people and reflect public interests. Political science uses empirical evidence and analytical tools to interpret political actions and systems.
Explanation:
Importance of Politics and Political Science
Politics and political science are pivotal because they deal with critical questions like who gets what, when, and how. Politics fundamentally addresses the allocation of resources and the mechanisms of decision-making within societies.
Political science is the systematic study of these processes, providing insights into government policies, institutional arrangements, and collective behaviors.
Knowledge in this field empowers citizens to engage meaningfully in their governance and to advocate for fairer, more representative systems.
Citizen engagement is essential for a functioning democracy, as it ensures that the government reflects the public interest. Understanding politics is not just for students at elite universities; it is crucial for all to recognize that political systems and conflicts deeply affect their lives.
Politics is not a spectator sport; active involvement and collective action can shift the balance of power towards ordinary people.
Political science students and scholars endeavor to answer why certain political actors behave as they do and to infer cause-effect relationships from empirical evidence.
The study of politics involves using tools such as probability, statistics, and logic to extract meaningful inferences from qualitative and quantitative data. For faculty, imparting this knowledge to students is a dual task of nurturing civic engagement and fostering academic inquiry into political behaviors and systems.
What are the factors affecting surface tension
Explanation:
Factors affecting surface tension includes;
There are three factors that affect surface tension.
Temperature- the surface tension of a liquid decreases with increase in temperature.
Soluble impurities - the presence of soluble impurities may increase or decrease the surface tension.
Insoluble impurities- insoluble impurities decrease the surface tension.