The equation that we can use in this case is:
y = v0 t + 0.5 a t^2
where, y is the height, v0 is initial velocity = 0, t is time, a is acceleration so that:
y = 0 + 0.5 * (300 m/s^2) * (7 s)^2
y = 7350 m
A rock falls freely from rest near the surface of a planet where acceleration due to gravity is 4.0 meters per second per second. what is the speed of this rock after it falls 32 meters?
The speed of the rock after it has fallen [tex]32\text{ m}[/tex] near the surface of the planet is [tex]\boxed{16\text{ m/s}}[/tex].
Explanation:
Given:
The acceleration due to gravity on the surface of the planet is [tex]4.0\text{ m/s}^2[/tex].
The distance through which the rock falls is [tex]32\text{ m}[/tex].
Concept:
As the rock falls near the surface of he planet, it falls freely under the action of the acceleration due to gravity i.e. the gravitational pull of the planet acting on the rock.
The acceleration due to gravity is different on the surface of the different planets. It depends on the mass and radius of the particular planet.
The final speed of the rock after falling through a particular distance is given by the third equation of motion.
[tex]\boxed{v_f^2=v_i^2+2gS}[/tex]
Here, [tex]v_f[/tex] is the final velocity of rock, [tex]v_i[/tex] is the initial velocity, [tex]g[/tex] is the acceleration due to gravity on planet and [tex]S[/tex] is the distance covered by the rock.
As the rock falls from the rest, the initial velocity of the rock will be zero.
Substitute the values in above expression.
[tex]\begin{aligned}v_f^2&=(0)^2+2(4)(32)\\v_f&=\sqrt{256}\\&=16\text{ m/s}\end{aligned}[/tex]
Thus, The speed of the rock after it has fallen [tex]32\text{ m}[/tex] near the surface of the planet is [tex]\boxed{16\text{ m/s}}[/tex].
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Laws of motion
Keywords:
acceleration, gravity, rock, planet, surface, equation of motion, initial, final, distance, velocity, 32 m, 16 m/s.
The speed of a rock falling 32 meters on a planet with 4.0 m/s² gravity is 16 m/s.
To determine the speed of a rock that falls freely from rest near the surface of a planet where the acceleration due to gravity is 4.0 meters per second squared, we can use the following kinematic equation:
v² = u² + 2as
Here:
v is the final velocityu is the initial velocity (0 m/s as the rock falls from rest)a is the acceleration due to gravity (4.0 m/s²)s is the distance fallen (32 meters)Substituting in the given values:
v² = 0 + 2 × 4.0 m/s² × 32 m
v² = 256
Taking the square root to find the speed:
v = √256
v = 16 m/s
Therefore, the speed of this rock after falling 32 meters is 16 meters per second.
Consider a book that weighs 15 N at rest on a flat table. How many newtons of support does the table provide?
A table provides a support force equal in magnitude and opposite in direction to the weight of the book on it; therefore, if the book weighs 15 N, the support force from the table is also 15 N.
The question involves understanding the forces involved when a book is placed on a table. If a book that weighs 15 N is at rest on a flat table, then the table must provide an equal and opposite force to support the book and keep it at rest, according to Newton's third law of motion. Therefore, the table provides a support force of 15 N upward to balance the weight of the book.
A bowling ball at rest is in equilibrium. Is the ball in equilibrium when it moves at constant speed in a straight-line path?
If you slow the motion of water molecules down, they are more likely to become
If you slow the motion of water molecules down, they are more likely to become ice crystal.
What is heat energy?Most people use the term "heat" to describe anything that feels warm, but according to science, heat is the movement of energy from a heated object to a cooler one.
Heat energy is the only thing that results from the movement of tiny particles known as atoms, molecules, or ions in liquids, solids, and gases. One substance can absorb heat energy from another, and the flow caused by a temperature difference between two objects is referred to as heat.
Hence, If you slow the motion of water molecules down, the heat energy from water molecule is taken away and they are cooled down. And more likely, water molecules are froze down and turns into ice crystal.
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The sun has more mass than earth, which has more mass than the moon. if the distance between each object was the same, which gravitational force would be the largest?
Objects on the moon's surface have an acceleration due to gravity one-sixth that on the earth's. What would the 50.0 kg boy weigh on the moon?
Answer: 80 N
Explanation:
The acceleration due to gravity on Earth is [tex]g=9.8 m/s^2[/tex]. On the Moon, it is 1/6 that on the Earth, so the acceleration due to gravity on the Moon is
[tex]g'=\frac{1}{6}g=\frac{1}{6}(9.8 m/s^2)=1.6 m/s^2[/tex]
The weight of the boy on the moon can be calculated as
[tex]W'=mg'[/tex]
where m=50 kg is the boy's mass. By substituting in the formula,
[tex]W'=(50 kg)(1.6 m/s^2)=80 N[/tex]
Ilya and Anya each can run at a speed of 8.30 mph and walk at a speed of 3.30 mph . They set off together on a route of length 5.00 miles . Anya walks half of the distance and runs the other half, while Ilya walks half of the time and runs the other half.
How long does it take Anya to cover the distance of 5.00 miles ?
How long does it take Ilya to cover the distance?
Find Ilya's average speed.
Many of the technological advances over the last 50 - 75 years have been in the area of weaponry and warfare, such as atomic/nuclear weapons, radar, biological weapons, etc. These advances have both positive and negative aspects. Which statement describes a negative aspect of these advances? A) The advances in body armor protect individuals and prevent deaths that previously could not be prevented. B) Advances in communication and transportation have made it easier to prevent attacks and rescue those who need be rescued. C) Advances in satellite imagery have made desired targets easy to hit with little destruction of innocent life and property. D) The lingering radiation after detonation of atomic weapons destroys the land and continues to harm people and animals long after the blast.
Answer:
D
Explanation:
How much heat energy (in megajoules) is needed to convert 7 kilograms of ice at –9°C to water at 0°C?
Why are glass fibers stronger than bulk glass?
If a scale of the solar system was built where 1 mm equaled 1 mile, could the model be practically built in a city?
Answer:
No
Explanation:
Given the relative scale (1mm = 1mile) lets calculate the size of the Sun and distance of planets from the Sun in mm.
Diameter of Sun = 864938 miles = 864938 mm = 864.938 meters
Distance of Earth from the Sun = 92955810 miles = 92955810 mm = 92.955 km = 57.75 miles
Distance of Jupiter from Sun = 480000000 miles = 480000000 mm = 480 km = 298 miles
As can be seen, the magnitude of scaled down distances is too huge to fit inside a city.
It will not be practically possible to make such a model.
Some scientists typically think of consciousness as a product of
Some scientists typically think of consciousness as a product of the brain's neural activity, particularly the activity of certain specialized regions of the brain such as the prefrontal cortex.
What is consciousness?Consciousness refers to the state of being aware of one's surroundings, thoughts, feelings, and perceptions. It is the subjective experience of being alive and aware of the world around us. Consciousness is often described as the quality or state of being aware of one's thoughts, feelings, and surroundings.
Consciousness can manifest in a variety of ways, including perception, attention, awareness, intentionality, and self-awareness. It is closely tied to our experiences of the world, and plays a central role in our ability to interact with our environment, communicate with others, and make decisions.
Despite its ubiquity in our everyday lives, consciousness is still not fully understood by scientists and philosophers. The study of consciousness is a topic of ongoing research and debate, with many theories attempting to explain how and why consciousness arises in the brain. Some theories suggest that consciousness is an emergent property of complex neural activity, while others propose that it may be a fundamental aspect of the universe itself.
Here in the Question,
Consciousness arises from the coordinated firing of neurons in these regions, which give rise to subjective experiences such as perception, thought, and emotion. Some scientists also believe that consciousness may involve the integration of information across different regions of the brain, as well as the ability to selectively attend to certain stimuli while filtering out others.
While there is still much that is not fully understood about the nature of consciousness, there is a growing body of research that suggests that it is closely tied to brain activity. For example, studies have shown that certain brain regions are more active during conscious states than during unconscious ones, and that the strength of the neural signals in these regions is correlated with the intensity of conscious experience. Other research has suggested that conscious experience may involve the synchronization of neural activity across different brain regions, or the modulation of neural activity by neurotransmitters such as dopamine and serotonin.
Therefore, Some scientists believe that consciousness is a byproduct of neuronal activity in the brain, particularly in some highly specialized areas of the brain like the prefrontal cortex.
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identify the chemical change below
a) a piece of wood burns in a fire
b) two pieces of paper are stapled together
c) water is removed by drying wet clothes on a laundry line
d) a large log is cut into boards
An object is projected horizontally at 8.0 m/s from the top of a 122.5 m cliff. how far from the base of the cliff will the object strike the ground?
1. Which of these statements is not a part of the Cell Theory?
a) The cell is the smallest living unit in all orgasims
b) All living things are made of cells
c) There are two main types of cells
d) All cells come from other pre-existing cells
2. _____ contain genetic material such as DNA.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
3. ____ plants are an example of me.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
4. ____ protists are an example of me.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
5. ____ your body cells are made of this type of cell.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
6. _____ contain cytoplasm.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
7. _____ contain membrane-bound organelles.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
8. _____ contain ribosomes.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
9. _____ Animals are an example of me.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
10. _____ fungi are an example of me.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
11. ____ bacteria are an example of me.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
12. _____ have a nucleus.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
13. ___ have a cell membrane.
a) Prokaryote only
b) Eukaryotes only
c) Both Prokaryotes and Eukaryotes
This answer deals with the key differences between prokaryotic and eukaryotic cells, in addition to explaining a part of the cell theory. Eukaryotic cells are usually found in complex organisms like plants, animals, fungi and protists, while prokaryotic cells are found in bacteria. The cell theory does not concern with the types of cells, hence 'there are two main types of cells' is not a part of the cell theory.
Explanation:1. The statement which is not a part of the Cell Theory is 'c) There are two main types of cells.'
2. Both Prokaryotes and Eukaryotes contain genetic material such as DNA.
3. Eukaryotes only plants are an example of me.
4. Eukaryotes only protists are an example of me.
5. Your body cells are made of Eukaryotes only type of cell.
6. Both Prokaryotes and Eukaryotes contain cytoplasm.
7. Eukaryotes only contain membrane-bound organelles.
8. Both Prokaryotes and Eukaryotes contain ribosomes.
9. Eukaryotes only Animals are an example of me.
10. Eukaryotes only fungi are an example of me.
11. Prokaryotes only bacteria are an example of me.
12. Eukaryotes only have a nucleus.
13. Both Prokaryotes and Eukaryotes have a cell membrane.
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What physical law(s) predicts the conservation of momentum?
If the planet mars is about 56 million kilometers from earth how long would it take for a radio wave sent from a space satellite circiling mars to reach earth
What element in the third period is a metalloid?
why would the size of a star affect its luminosity
The size of a star directly affects its luminosity because larger stars have a larger surface area and can emit more light and heat. On the other hand, smaller stars have a smaller surface area and emit less light, resulting in a lower luminosity.
Explanation:The size of a star affects its luminosity because the luminosity of a star is directly related to its surface area. Larger stars have a larger surface area, which allows them to emit more light and heat, resulting in a higher luminosity. On the other hand, smaller stars have a smaller surface area and emit less light, leading to a lower luminosity.
For example, let's consider two stars of the same temperature, but different sizes. The larger star will have a greater luminosity because it has a larger surface area from which it can radiate energy. Conversely, the smaller star will have a lower luminosity due to its smaller surface area.
Therefore, the size of a star directly impacts its luminosity, with larger stars being more luminous than smaller stars.
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How long does it take our solar system to make a complete orbit around our galaxy?
The international space station makes 15.65 revolutions per day in its orbit around the earth. assuming a circular orbit, how high is this satellite above the surface of the earth?
The International space station is located at the height of [tex]\boxed{369\,{\text{km}}}[/tex] above the surface of the Earth.
Further Explanation:
The height of the international space station above the surface of the earth is given by the Kepler’s Law of planetary motion. According to this law, the square of time period of the satellite is directly proportional to the cube of the radius of the circular path of the satellite.
Given:
The speed of revolutions made by the International space station is [tex]15.65\,{{{\text{rev}}}\mathord{\left/{\vphantom{{{\text{rev}}}{{\text{day}}}}}\right.\kern-\nulldelimiterspace}{{\text{day}}}}[/tex] .
Concept:
The angular speed of rotation of the International space station is:
[tex]\begin{aligned}\omega&=2\pi\times\frac{{15.65}}{{24\times60\times 60}}\,{{{\text{rev}}}\mathord{\left/{\vphantom{{{\text{rev}}}{{\text{sec}}}}}\right.\kern-\nulldelimiterspace}{{\text{sec}}}}\\&=2\pi\times1.811\times{10^{ - 4}}\,{{{\text{rad}}}\mathord{\left/{\vphantom{{{\text{rad}}}{{\text{sec}}}}}\right.\kern-\nulldelimiterspace}{{\text{sec}}}}\\\end{aligned}[/tex]
The time period of rotation of the International space station is:
[tex]T=\frac{{2\pi }}{\omega }[/tex]
Substitute [tex]\omega[/tex] in above expression.
[tex]\begin{aligned}T&=\frac{{2\pi}}{{2\pi\times1.811\times{{10}^{ - 4}}\,}}\\&=5520.7\,{\text{s}}\\&\approx{\text{5521}}\,{\text{s}}\\\end{aligned}[/tex]
The expression for the Kepler’s law is:
[tex]\begin{aligned}{T^2}&=\left({\frac{{4{\pi ^2}}}{{GM}}}\right){R^3}\\R&={\left({\frac{{GM{T^2}}}{{4{\pi^2}}}}\right)^{\frac{1}{3}}}\\\end{aligned}[/tex]
Here, [tex]G[/tex] is the gravitational constant, [tex]M[/tex] is the mass of the Earth.
Substitute the values in above expression.
[tex]\begin{aligned}R&={\left({\frac{{\left( {6.67\times{{10}^{ - 11}}}\right)\times\left({5.98\times{{10}^{24}}}\right)\times{{\left( {5521}\right)}^2}}}{{4\times{{\left({3.14}\right)}^2}}}}\right)^{\frac{1}{3}}}\\&={\left({\frac{{1.21\times{{10}^{22}}}}{{39.48}}}\right)^{\frac{1}{3}}}\\&=6.74\times{10^6}\,{\text{m}}\\\end{aligned}[/tex]
The radius of the Earth is [tex]6.371\times{10^6}\,{\text{m}}[/tex] .
The height of space station above the surface of Earth is given below:
[tex]\begin{aligned}h&=\left({6.74\times{{10}^6}}\right)-\left({6.371\times{{10}^6}}\right)\\&=3.69\times{10^5}\,{\text{m}}\\&=3{\text{69}}\,{\text{km}}\\\end{aligned}[/tex]
Thus, the International space station is located at the height of [tex]\boxed{369\,{\text{km}}}[/tex] above the surface of the Earth.
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Gravitation
Keywords:
International space station, 15.65 revolutions, circular orbit, around the earth, high, satellite, above the surface, 5521 s, 369 km.
How many joules are in 1 kilowatt hour?
The earth is made mostly of metals and rocks. Where did this material come from? It was made by nuclear fission of uranium and other radioactive materials. It was produced in the Big Bang. It was created by chemical reactions in interstellar space. It was made by our Sun. It was produced by nuclear fusion in stars.
The Earth is composed largely of metals and silicate rock, primarily formed from hydrogen and helium, the simplest elements present from the inception of the universe during the Big Bang. Over time, inside the stars, nuclear reactions fusing these elements resulted in the creation of heavier elements, such as silicon and iron. Elements heavier than iron are synthesized through the powerful explosions of supernovas.
Explanation:The earth is composed largely of metals and silicate rock which were formed from hydrogen and helium, the simplest elements present from the inception of the universe during the Big Bang. Over time, inside the vastness of the stars, nuclear reactions fusing these elements resulted in the creation of heavier elements, such as silicon and iron which constitutes most of Earth's materials. This process is known as nucleosynthesis.
As time passes, the proportion of these heavier elements in the raw materials that make new stars and planets increases. Therefore, it can be said that Earth, with its abundance of heavier elements, was only possible after generations of stars had a chance to make and recycle their heavier elements.
Finally, elements heavier than iron are synthesized through the powerful explosions of supernovas. So, in essence, all of Earth's components and our very existence can be traced back to the stars and the nuclear reactions within them.
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An object placed on an equal-arm balance requires 12 kg to balance it. when placed on a spring scale, the scale reads 12 kg. everything (balance, spring scale, set of masses and object) is now transported to the moon, where the force of gravity is one-sixth that on earth. the new readings of the balance and spring scale (respectively) are:
a girl pushes a cart to the left a 100-N force. a boy pushes it to the right with a 50-N force. The net force exerted on the cart is
what will happen to the soccer ball as it rolls down the ramp?
The question is on science there isnt a choice for science
Explanation of what happens to a soccer ball as it rolls down a ramp due to the gravitational force.
When a soccer ball rolls down a ramp, it behaves similarly to a basketball rolling down a playground slide. As the soccer ball starts rolling down the ramp, its velocity increases due to the force of gravity pulling it towards the Earth's center. This gravity is a consistent force that works on the ball acting down the ramp. On a straight slope, the ball's velocity will increase, and the velocity will be the greatest just before the ball begins to rise up another ramp or before it comes to a stop. The acceleration of the ball is constant while it is on the straight section of the ramp assuming no air friction or rolling resistance. As the ball moves down the ramp, it is transitioning from a state of higher gravitational potential energy to one with higher kinetic energy; the greatest kinetic energy is present when the ball is at the bottom of the ramp, moving at its fastest speed. If the ramp is altered in height or angle, so too will the path and velocity of the soccer ball change.
Who is credited with being the first person to accurately determine earth's circumference?
What color of light in the visible spectrum appears brightest?
) what is kinetic energy, and how does it differ from potential energy?
A river has a steady speed of 0.500 m/s. a student swims upstream a distance of 1.00 km and swims back to the starting point. if the student can swim at a speed of 1.20 m/s in still water, how long does the trip take? compare this with the time the trip would take if the water were still.
The student would take approximately 33.6 minutes to swim 1 km upstream and then 1 km downstream. Comparatively, if the water were still, the round trip would only take about 27.8 minutes.
Explanation:To calculate the time it takes for the trip upstream and downstream, we must consider the effect of the river's speed on the swimmer's speed.
Upstream: When the student swims upstream, the river speed works against his own speed. Here, we subtract the river's speed from the student's speed: effective speed = 1.20 m/s - 0.500 m/s = 0.700 m/s. The distance he covers is 1.00 km = 1000 m. The time taken going upstream is then t = Distance/Speed = 1000 m / 0.700 m/s = 1428.6 s.
Downstream: When swimming downstream, the river speed aids the student's speed. Now, we add the student's swimming speed to the river's speed: effective speed = 1.20 m/s + 0.500 m/s = 1.70 m/s. With the same distance to cover, the time taken to swim downstream is: t = 1000m / 1.70 m/s = 588.24 s.
In total, the round trip time amounts to: ttotal = 1428.6 s + 588.24 s = 2016.84 s, which is approximately 33.6 minutes.
If the water were still, the student would swim at his own speed both ways: t = 1000 m / 1.20 m/s = 833.33 s each way. So, the total round trip would take: ttotal = 833.33 s × 2 = 1666.66 s, or approximately 27.8 minutes.
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The round trip takes 2017 seconds with the current and 1666 seconds in still water. Swimming upstream and downstream times factor into this calculation.
To determine how long the trip takes for a student swimming upstream and then back downstream, we need to consider both the swimmer’s speed and the speed of the river current.
When swimming upstream:Swimmer's speed relative to ground = Swimmer's speed in still water - River's speed = 1.20 m/s - 0.50 m/s = 0.70 m/s.
Time taken to swim upstream = Distance / Speed = 1000 m / 0.70 m/s = 1429 s.
When swimming downstream:Swimmer's speed relative to ground = Swimmer's speed in still water + River's speed = 1.20 m/s + 0.50 m/s = 1.70 m/s.
Time taken to swim downstream = Distance / Speed = 1000 m / 1.70 m/s = 588 s.
Total time for the round trip = Time upstream + Time downstream = 1429 s + 588 s = 2017 s.
If the water were still, the student's speed would be 1.20 m/s in both directions:
Time for one direction in still water = Distance / Speed = 1000 m / 1.20 m/s ≈ 833 s.
Total time for the round trip in still water= 833 s + 833 s = 1666 s.
Therefore, it takes 2017 s to complete the trip with the current, compared to 1666 s without the current.