# Kinetic Energy

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1. Nov 22, 2015

### NatalieWise123

1. The problem statement, all variables and given/known data
A ball with a mass of 2.3 kg is thrown into the air. If the ball rises to a maximum height of 15 m before stopping and coming back down, how much kinetic energy did the ball have initially?

2. Relevant equations
KE=0.5*mass*velocity^2

3. The attempt at a solution
I don't think it's possible because no velocity is given and you can't find it because there is no time given. Am I missing something?

2. Nov 22, 2015

### AhmirMalik

Why dont you just aply the conservation of the energy?

$$E_{i}=E_{f}$$

3. Nov 22, 2015

### NatalieWise123

Can you explain further? I don't really understand.

4. Nov 22, 2015

### AhmirMalik

The total energy of the system has to be conserved. That means, the total initial energy must be equal to the final total energy.

$$\frac{m(v_{i})^2}{2}+mgh_{i}=\frac{m(v_{f})^2}{2}+mgh_{f}$$

where $$\frac{m(v_{i})^2}{2}$$ is what you are looking for.

5. Nov 22, 2015

Exactly as above. You have to remember that energy is conserved, so the potential energy gained by the ball being thrown up, is equal to the kinetic energy lost and vice versa. Essentially in this problem, your answer can be obtained using $KE_i = PE_f$ Which is the same as what the person above did, but by taking the hand as the inial starting reference fram where PE=0, some terms fall out, leaving you with $\frac{1}{2}mv_i^2 = mgh_f$

6. Nov 23, 2015

### NatalieWise123

OK so I can do 2.3*9.8*15= 338.1 J which is final PE but since they're equal that is the answer for initial KE?

7. Nov 23, 2015

Yes that answer is correct. It is more correct to say that that is the "potential energy gained" rather than "final potential energy" as it is technically a change in energy, but that's just semantics I guess. But yes, since energy is conserved it is equal to the kinetic energy you are looking for.

8. Jun 20, 2016

### Hangtime

Can it be said that when components that contain a like kind of kinetic energy assemble together, the sum of that energy is shared between them? Abstractly it seems that this effect can be observed in every kind of cohesive bond within a physical transfer such as thermal transfer, pressure transfer and density transfers.

9. Jun 20, 2016

### SteamKing

Staff Emeritus
Yes, you are. The ball doesn't simply jump out of your hand. It must be propelled upward with an initial velocity. Knowing how far up the ball travels allows one to calculate the initial velocity. Sometimes, not all the facts are presented in neat packages suitable for plugging and chugging.