# A cannon ball and a moving train.

1. Aug 5, 2005

### dazzclub

Hi i was wondering if you guys could help me out on this i think i know the result but i would like to see if your guys agree.

heres the situation:

A cannon is positioned vertical on top of a moving train, the cannon shoots the ball straight up in the air. Where does the ball land, behind the train, next to the train or lands roughly in the same place where the ball was shot from.

cheers guys

2. Aug 5, 2005

### Danger

This would appear to be a variant upon the question of figuring out the bomb-release point for an aeroplane, except... you would have to supply a muzzle velocity and cannonball mass/shape. After all, if you shoot the thing fast enough it will never come back.

3. Aug 5, 2005

### dazzclub

no details on variables sorry

hmmmm, I have no details on the variables used in this situation, but if we did, are we safe to say the cannon ball will land behind the moving train.

In no way will the ball land roughly in the same place where it was shot aka back on the moving train?

cheers

4. Aug 5, 2005

### bomba923

Hmm---assuming the train is in linear motion...and ideal+certain other conditions/assumptions....
Let $$\bar a$$ represent the average acceleration of the train between the times of "shooting of the cannon" and the "landing of the cannonball".

*If $$\bar a = 0$$, the cannon will land in the same place from which it was shot (cannonball will hit the cannon if you don't move the cannon!).
*If $$\bar a > 0$$, the the cannon will land behind the train.
*If $$\bar a < 0$$ the cannon will land in front of the train.
I feel like I gave away the answer; I shall explain if need be

If you explain what conditions there are for the motions of the train&cannonball...air resistance? constant accelerations? Apparently I have to make quite a lot of assumptions myself when answering this question (not familiar with the frame of reference you have not defined!)
b/c

Last edited: Aug 5, 2005
5. Aug 5, 2005

### Rainbow

Well, the cannon ball shot is a projectile right.

And we know that the horizontal velocity of a projectile is constant (assuming that the air resistent is zero).

Now when the cannon ball is shot from the cannon (vertically upwards) then the horizontal velocity of the cannon ball relative to that of the train will be zero (note: we are assuming that the train is not accelerating).

So, range of the cannon ball (the projectile) will be equal to the displacement of the cannon ( i.e. the place where the ball was shot from).

Hence, the ball will land roughly on the same place where the ball was shot from.

6. Aug 5, 2005

### FredGarvin

If neglecting resistance, the train does not accelerate and the cannon is perfectly vertical, the cannon ball will have the same horizontal speed as the train. Therefore it will land approximately in the same place it was fired from.

7. Aug 5, 2005

### catalyst55

It's much like jumping in a train moving uniformly. Next time you're in the train, jump up, and take notice of where you land. Do you think you'll end up at the back of the train because the train is moving forward? Dont think so.

The train is a closed inertial system, much like the earth (i.e. your frame of reference is the train, not the outside of the train).

8. Jan 1, 2009

### Atari2600

Hmm... but the question was about a cannon positioned on TOP of a moving train so it is not at all like jumping INSIDE a moving train. The train and the air inside the train are moving at totally different speeds in relation to the air outside of the train. Therefore if you shoot away from the moving object and it's moving air and into the air that is not moving with train you end up with a great deal of resistance. Of course, this problem cannot be answered accurately without more information but I think the basis of the original question was just whether or not the cannon ball would land back on the cannon... I say not even close, but can't say for sure where it would land.

Now, if I were standing next to the train tracks and observed someone firing a cannon ball into the air as the train as it passed, I do not think it could be accurately predicted where the ball would hit the ground without more details.

9. Jan 2, 2009

### Ranger Mike

Coriolis effect and Gravity will dramatically impact ( sorry for the pun) on where the round ends up....