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Homework Help: Relative velocity of a ball on a train

  1. Aug 3, 2016 #1
    1. The problem statement, all variables and given/known data
    A train is travelling east along a straight run of track at 72.0 km/hr. Inside, two siblings 1.9 m apart are playing catch directly across the aisle. The kid wearing a P.J.Harvey T-shirt throws the ball horizontally north. The ball crosses the train and is caught 0.75 s later by her little brother. (Ignore any effects of gravity or friction.) Find the magnitude of the ball's velocity from the little brother's point of view.

    2. Relevant equations
    1. xf = xi + ViΔt + 1/2ax(Δt)2
    2. a2 = b2 + c2

    3. The attempt at a solution
    I used the first equation to calculate the velocity of the ball in the y-axis. I assumed that xi = ax = 0 and got 2.5 m/s. I then used Pythagoras and head-to-tail vector addition to get the actual speed and direction of the ball, taking speed in the x-axis as the speed of the train (20m/s). I took the brother to be moving at the same speed and direction as the train. My final answer was 40 m/s.

    I know this is the wrong answer but I can't work out why. Any advice?

  2. jcsd
  3. Aug 3, 2016 #2


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    Science Advisor

    What about a simpler question; what is the balls velocity from the boy's point of view before the ball is thrown? Is the ball moving relative to the boy?

    The velocity of the train is irrelevant as the boy, girl, and train are not moving relative to each other. Similarly, if they were playing catch at the train station the earths motion relative to the sun or the solar systems velocity relative to the centre of the milky way isn't relevant: the velocity the boy sees is relative to himself.
  4. Aug 3, 2016 #3
    That was the way I thought about it at first, which got me my 2.5 m/s. I thought because the boy was "technically" stationary it wouldn't affect the true velocity of the ball.
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