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17 May, 04:22

It takes 3 s for a rock to hit the ground when it is thrown straight up from a cliff with an initial velocity of 8.63 m/s. How long a time would it take to reach the ground if it is thrown straight down with the same speed?

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  1. 17 May, 07:11
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    h = height of the cliff

    Consider upward direction as positive and downward direction as negative

    Consider the motion of rock thrown straight up:

    Y = vertical displacement = - h

    v₀ = initial velocity = 8.63 m/s

    a = acceleration = - 9.8 m/s²

    t = time taken to hit the ground = 3 s

    Using the equation

    Y = v₀ t + (0.5) a t²

    - h = (8.63) (3) + (0.5) ( - 9.8) (3) ²

    h = 18.21 m

    Consider the motion of rock thrown down:

    Y' = vertical displacement = - 18.21

    v'₀ = initial velocity = - 8.63 m/s

    a' = acceleration = - 9.8 m/s²

    t' = time taken to hit the ground = ?

    Using the equation

    Y' = v'₀ t' + (0.5) a' t'²

    - 18.21 = ( - 8.63) t' + (0.5) ( - 9.8) t'²

    t' = 1.2 s
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