Find Energy of 2kg Stone After Projection from 15m Cliff

In summary, the conversation discusses how to find the energy possessed by a 2 kg stone that is projected horizontally with a speed of 20 m/s from a 15 m cliff just before it touches the ground. The solution is found by considering the initial and final energies to be equal and taking into account the loss of potential energy as the stone falls. The correct answer is 400J.
  • #1
lingling
22
0

Homework Statement



A stone of mass 2 kg is projected horizontally with a speed of 20 m/s from a cliff which is 15 m above the ground. Find the energy possessed by the stone just before touching the ground.

A. 400J
B. 500J
C. 600J
D. 700J

Homework Equations





The Attempt at a Solution


I can't get the answer. How can I achieve it?
I think 'just before touching the ground' means when the stone is still moving, but I don't know the velocity at this instant. And at the same time, the stone is losing potential energy, how can I manage this?
 
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  • #2
HINT: Inital Energy = Final Energy

Consider 'just before the stone touches the ground' to be the stone has actually hit the ground but not lost any kinetic energy, the instant the stone touches the ground.
 
  • #3
Ah... I've got it!
Thanks a lot!
 
  • #4
lingling said:
Ah... I've got it!
Thanks a lot!
My pleasure :smile:
 

What is the formula for finding the energy of a 2kg stone after being projected from a 15m cliff?

The formula for finding the energy of a moving object is KE = 1/2 * m * v^2, where KE is kinetic energy, m is the mass of the object, and v is the velocity of the object.

How do you calculate the velocity of the stone after being projected from a 15m cliff?

To calculate the velocity of the stone, you can use the formula v = √(2 * g * h), where g is the acceleration due to gravity (9.8 m/s^2) and h is the height of the cliff (in this case, 15m).

What is the mass of the stone if its energy after projection is known to be 150 joules?

To find the mass of the stone, we can rearrange the formula for kinetic energy to m = 2 * KE / v^2. Substituting the given values, we get m = 2 * 150 J / (√(2 * 9.8 m/s^2 * 15m))^2. Solving this equation, we get a mass of approximately 0.97 kg.

How does the height of the cliff affect the energy of the stone after projection?

The higher the cliff, the more potential energy the stone has before being projected. This potential energy is then converted into kinetic energy as the stone falls, resulting in a higher energy at the bottom of the cliff compared to a lower cliff.

Can the energy of the stone after projection be greater than its initial potential energy at the top of the cliff?

No, according to the law of conservation of energy, energy cannot be created or destroyed, only transferred. Therefore, the energy at the bottom of the cliff cannot be greater than the initial potential energy at the top.

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