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    Rain falling vertically hits the windows of an intercity train which is travelling at 50m/s. A passenger watches the rain streaks on the window and estimates them to be an angle of 20 degrees to the horizontal.

    (i) Calculate the speed the rain would run down a stationary window.
    (ii) The train starts to slow down with a uniform deceleration and 1.5 minutes later the streaks are at 45 degrees to the horizontal. What is the deceleration of the train??

    Could you draw a diagram , becuase it will help me.


    It doesn't look like M1 stuff, it's relative motion isn't it? Which exam board are you in?

    Let \bold \fs3 \vec{u},\  \vec{v} be the velocity of the train and velocity of the rain respectively.
    \bold \fs3 \vec{v} is vertically downwards, and \bold \fs3 \vec{u} is horizontal. Please draw a diagram for yourself.

    i) So velocity of the rain respects to the train will be \fs3 \vec{v} - \vec{u} which makes an angle of 20 degrees with the horizontal.
    -> tan20 = v/u -> v = utan20 (u, v without arrows are speeds)

    ii) v = u'tan45 -> u' = v/tan45 = utan20/tan45
    t = 1.5 mins = 90s
    -> a = (u' - u)/t
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Updated: November 20, 2005

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