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8 December, 05:24

A very strong, but inept, shot putter puts the shot straight up vertically with an initial velocity of 11.1 m/s. How long does he have to get out of the way if the shot was released at a height of 2.27 m, and he is 1.96 m tall?

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  1. 8 December, 05:48
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    We need to use the kinematic equation

    S=ut + (1/2) at^2

    where

    S=displacement (+=up, in metres)

    u=initial velocity (m/s)

    t=time (seconds)

    a=acceleration (+=up, in m/s^2)

    Substitute values

    S=displacement = 1.96-2.27 = - 0.31 m (so that shot does not hit his head)

    u=11.1

    a=-9.81 (acceleration due to gravity)

    -0.31=11.1t + (1/2) (-9.81) t^2

    Rearrange and solve for t

    -4.905t^2+11.1t-0.31=0

    t=-0.02756 or t=2.291 seconds

    Reject the negative root to give

    t=2.29 seconds (to 3 significant figures)
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