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10 March, 15:36

A parachutist bails out and freely falls 50 m. Then the parachute opens, and thereafter she deceler - ates at 2.0 m/s2. She reaches the ground with a speed of 3.0 m/s. (a) How long is the parachutist in the air? (b) At what height does the fall begin?

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  1. 10 March, 17:50
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    a) The parachutist in the air for 12.63 seconds.

    b) The parachutist falls from a height of 293 meter.

    Explanation:

    Vertical motion of parachutist:

    Initial speed, u = 0m/s

    Acceleration, a = 9.81 m/s²

    Displacement, s = 50 m

    We have equation of motion, v² = u² + 2as

    Substituting

    v² = 0² + 2 x 9.81 x 50

    v = 31.32 m/s

    Time taken for this

    31.32 = 0 + 9.81 x t

    t = 3.19 s

    After 50m we have

    Initial speed, u = 31.32m/s

    Acceleration, a = - 2 m/s²

    Final speed, v = 3 m/s

    We have equation of motion, v² = u² + 2as

    Substituting

    3² = 31.32² - 2 x 2 x s

    s = 243 m

    Time taken for this

    3 = 31.32 - 2 x t

    t = 9.44 s

    a) Total time = 3.19 + 9.44 = 12.63 s

    The parachutist in the air for 12.63 seconds.

    b) Total height = 50 + 243 = 293 m

    The parachutist falls from a height of 293 meter.
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