# Homework Help: A ball is thrown upwards and another dropped

1. Oct 5, 2012

### Nubcake

Simultaneously , a ball is thrown upwards and another dropped from rest. Which one hits the ground moving faster?

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The ball thrown upwards because during it's descent as it starts to fall back down it's velocity is increasing due to acceleration from gravity hence the greater the distance the greater velocity it will achieve before hitting the ground

I'm not confident with my anwser ; is it safe to say its velocity is increasing by 9.8 m s-1 every second?

Can someone please give me a detailed explanation on this?

2. Oct 5, 2012

### BruceW

well, really its velocity is changing by 9.8m/s every second. so the velocity is not necessarily increasing.

Also, about the problem generally, we are not supposed to just give you the answer on this forum. But we can help. My advice is to think about energy. Start thinking of things you know about energy in this situation.

3. Oct 5, 2012

### Nubcake

Changing is what I meant , how does energy relate to this question? It is to do with projectiles , are you referring to kinetic energy of the ball?

4. Oct 5, 2012

### Staff: Mentor

In addition to thinking about the energies involved, you can also ask yourself what the velocity of the thrown ball will be when it passes you on the way down. Is it moving faster at that point than the ball that you dropped?

As for the equation, use the kinematic equation of motion for constant acceleration (gravity's acceleration is constant for this problem) -- use the one that relates the final velocity to initial velocity and acceleration, and the one that relates final position to initial position, velocity and acceleration...

5. Oct 5, 2012

### BruceW

Yes, the ball has kinetic energy and one other kind of energy. I was hinting about energy, because I think your teacher will be more happy if you give an explanation using the concept of energy. Your answer: "The ball thrown upwards because during it's descent as it starts to fall back down it's velocity is increasing due to acceleration from gravity hence the greater the distance the greater velocity it will achieve before hitting the ground" Is true, but not very qualitative. A better answer would be to say something definite about the difference in kinetic energy of the two balls when they hit the ground.

Edit: I meant to say quantitative, not qualitative. Those two are easy to get mixed up :)

Last edited: Oct 5, 2012
6. Oct 5, 2012

### Nubcake

I'm positive that the velocity of the ball that was thrown up on its way down will be greater than the ball that was dropped from rest but another person who I posed this question says otherwise that both balls would hit the ground with the same velocity since acceleration is constant for both balls regardless of the height it was dropped from or thrown up

So it is the ball thrown up then? Could anyone explain why relating to projectiles because we haven't covered energy in my class yet so It must be to do with velocity and acceleration

Last edited: Oct 5, 2012
7. Oct 5, 2012

### ehild

If you haven't covered energy yet in class, you really need to think in terms of velocity, acceleration and time. You are right, the thrown ball will hit the ground with greater speed than the dropped one, but why?
Think: the ball thrown up will rise , loses its speed, and starts to fall back from a higher position than the other ball which was dropped. From higher position, the ball falls for longer time. How is the time and speed of falling bodies related?
You can calculate the final height of the ball if it was thrown up with speed Vo from a tower of height H. And then, how long does it fall to the ground. And what will be its final speed. And what is the speed of the other ball which was dropped from height H.

ehild

8. Oct 5, 2012

### Muphrid

ehild has the correct explanation as far as avoiding energy explanations. Here's an alternative, though:

Isn't it true that if you throw a ball in the air that, by the time it falls to the same height you threw it from, it has the same speed (just in a different direction)? You should see that this is true just from the symmetry of the parabolic trajectory.

Now, consider the limiting case of the balls being released from a small distance above the ground.

9. Oct 5, 2012

### BruceW

Other people have given some good advice. Your friend is right that the acceleration is constant for both, but as you observed, the change in velocity per second is equal to the acceleration. and you are right that the greater distance means greater velocity will build up.