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Confusion in relative motion

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Let $V_{BT} = V \vec j = V_B - V_T$

And $V_{MT}=0$

Hence $V_{BM}= V\vec j$

Then how the ball appreas to be moving backward or ahead of the person .

asked Apr 4, 2017 in Physics Problems by koolman (4,196 points)

1 Answer

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Use a frame of reference in which the train is at rest at the moment the ball is thrown. In this frame the ball always has zero horizontal velocity.

Then if the train (and passenger) are accelerating, they move forward in the frame of reference, while the ball stays in the same horizontal position. Relative to the train and passenger, the ball moves backwards.

If the train and passenger are decelerating, they move backward in the frame of reference, while the ball retains the same horizontal position. Relative to them the ball moves forwards.

answered Apr 5, 2017 by sammy gerbil (26,678 points)
selected Apr 6, 2017 by koolman
can we prove it mathematically .
Yes you can, if you want to. But I don't see any benefit in doing so.
I tried it above , but don't got the result.
Please explain in words what your attempt means, I don't understand it.
$V_{BT} = V \vec j = V_B - V_T$
$V_{BT}=$ velocity of ball with respect to train

And $V_{MT}=0$
$V_{MT}=$ velocity of man with respect to train

Hence $V_{BM}= V\vec j$
$V_{BM}=$ velocity of ball wrt man .
As its direction is always in vertical direction.Then how can ball move in horizontal direction .
The motion of the ball is vertical relative to the passenger at the moment of release,  but it does not remain vertical relative to the passenger if the speed of the train changes after the ball is released. You are confusing two different frames of reference.
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