1792
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If a train were travelling at a certain speed and as it passed point A a machine fired a tennis ball out of the back of the final carriage, and also at point A an identical machine that was stationary fired another tennis ball in the same direction which ball would travel further?

Both machines exert the same force, both balls are identical mass and ignoring air resistance.
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(Original post by 1792)
If a train were travelling at a certain speed and as it passed point A a machine fired a tennis ball out of the back of the final carriage, and also at point A an identical machine that was stationary fired another tennis ball in the same direction which ball would travel further?

Both machines exert the same force, both balls are identical mass and ignoring air resistance.
There's no horizontal acceleration as we're ignoring air resistance, so the horizontal motion only stops when it hits the ground. Which one will hit the ground first?

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lerjj
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(Original post by Arithmeticae)
There's no horizontal acceleration as we're ignoring air resistance, so the horizontal motion only stops when it hits the ground. Which one will hit the ground first?

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I think the machines are meant to be at the same height and the train is travelling parallel to horizontal. So they'll actually hit the ground at the same time. It's more obvious that that.
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(Original post by lerjj)
I think the machines are meant to be at the same height and the train is travelling parallel to horizontal. So they'll actually hit the ground at the same time. It's more obvious that that.
Ah right, guess I misread it. would it just be the first one as the ball was travelling at the same speed as the train (relative to a stationary observer) so it accelerates from the speed of the train but the other ball accelerates from rest?

Edit - Is the train travelling with the motion of the ball or against it?
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Stonebridge
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Although I suspect the writer of this question has an answer in mind, it does actually depend on the relative speed of the train and the speed at which the ball is ejected. These are not given so it isn't actually possible to give a definite answer. For example, what if the train were travelling at more than twice the speed of the ball from the machine?
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K_o_46
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The second ball will travel further.

This is because the first ball has an initial speed equal to that of the train. For example lets say the train was travelling at 30 m/s, we take u as -30 because it is moving in the opposite direction of the displacement were looking for. Ball 2 has u=0

Next since the two balls are identical in mass and experience the same force by the machines we can say that theirs accelerations are equal (f=ma). Lets assume an acceleration of +80m/s^2 with an impact time of 2 seconds (acceleration due to machine lasts for 2 seconds)

s= ut + 0.5at^2

Therefore ball 1 travels (-30x2)+ (0.5x80x2)= 20m

ball 2 travels
(0x2)+ (0.5x80x2)=80m after 2 seconds

afyer the two they both remain at constant speed assuming no air resistance so ball 2 will remain further
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lerjj
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(Original post by Stonebridge)
Although I suspect the writer of this question has an answer in mind, it does actually depend on the relative speed of the train and the speed at which the ball is ejected. These are not given so it isn't actually possible to give a definite answer. For example, what if the train were travelling at more than twice the speed of the ball from the machine?
The machines are described as identical, all that matters is that the train is moving in the opposite direction to the two balls, which is implied by the machine being located on the back of the carriage. Because the train's speed relative to the ground has the opposite sign to the two balls, you don't need any numbers to give a qualitative answer.
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Stonebridge
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(Original post by lerjj)
The machines are described as identical, all that matters is that the train is moving in the opposite direction to the two balls, which is implied by the machine being located on the back of the carriage. Because the train's speed relative to the ground has the opposite sign to the two balls, you don't need any numbers to give a qualitative answer.
Yes you do. Have another think about it. The question asks which ball travels further. They are both in flight for the same period of time, so the distance travelled by either ball only depends on the magnitude of its horizontal velocity. This in turn depends on the difference between the speed of the train and the speed of ejection of the ball. If the train were at rest both balls would travel the same distance. No problem. If the train were moving at the same speed as the ejection speed the ball would have zero horizontal velocity and would drop to the ground vertically. This would be the shortest distance possible for the ball to travel. Now think what happens if the train moves even faster.
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(Original post by Stonebridge)
Yes you do. Have another think about it. The question asks which ball travels further. They are both in flight for the same period of time, so the distance travelled by either ball only depends on the magnitude of its horizontal velocity. This in turn depends on the difference between the speed of the train and the speed of ejection of the ball. If the train were at rest both balls would travel the same distance. No problem. If the train were moving at the same speed as the ejection speed the ball would have zero horizontal velocity and would drop to the ground vertically. This would be the shortest distance possible for the ball to travel. Now think what happens if the train moves even faster.
Woops. I don't think they considered that when writing the question .
Regardless, you could argue that 'travelling further' means travelling further in what we're calling the positive direction.
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Stonebridge
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(Original post by lerjj)
Woops. I don't think they considered that when writing the question .
Regardless, you could argue that 'travelling further' means travelling further in what we're calling the positive direction.
Yes of course. And that's what I meant in my first reply when I said I thought the person who wrote the original question had a particular answer in mind. However, my point was that this answer is not necessarily correct if one allows other possibilities. The question doesn't forbid this so the "alternative" answers are valid. If this was an open question then all these possibilities should be considered. If not, then it was a poor question.
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(Original post by Stonebridge)
Yes of course. And that's what I meant in my first reply when I said I thought the person who wrote the original question had a particular answer in mind. However, my point was that this answer is not necessarily correct if one allows other possibilities. The question doesn't forbid this so the "alternative" answers are valid. If this was an open question then all these possibilities should be considered. If not, then it was a poor question.
But if it was a totally open question we'd also have to state what the balls are travelling relative to. Ball 1 travels the same distance relative to the train, as Ball 2 travels relative to the ground. You'd also have to allow that as a potential answer. At the end of the day, writing questions to exclude all these is fairly difficult/ long-winded, and the obvious answer is probably the one being looked for.
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(Original post by lerjj)
But if it was a totally open question we'd also have to state what the balls are travelling relative to. Ball 1 travels the same distance relative to the train, as Ball 2 travels relative to the ground. You'd also have to allow that as a potential answer. At the end of the day, writing questions to exclude all these is fairly difficult/ long-winded, and the obvious answer is probably the one being looked for.
Conclusion.
Writing good, unambiguous, questions is not easy.
This question is evidence of that.
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DrQuantum
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In a circumstance where the ball is traveling at a lower speed then the train relative to the stationary observer outside, it would be the stationary fired ball that would appear to travel further relative to the stationary observer.

However if for example the train was moving at 700ms^-1 (I know this is not practical by the way / It's a thought experiment)
and the tennis ball was ejected at 20ms^-1 and traveled for 5 seconds before hitting the ground in both cases. the ball from the train would have traveled a distance of:
(700-20)(5) = (680 * 5) = 3400m ahead of the post.

And the stationary one would travel a distance of:

20*5 = 100 m behind the post.

So the answer can vary, you must give more information.
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