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27 November, 17:35

A rubber ball with a mass of 0.145 kg is dropped from rest. From what height (in m) was the ball dropped, if the magnitude of the ball's momentum is 0.800 kg · m/s just before it lands on the ground?

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  1. 27 November, 20:18
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    1.55 m

    Explanation:

    Momentum: This can be defined as the product of mass of a body and it velocity. the S. I unit of momentum is kgm/s.

    Mathematically,

    Momentum can be represented as,

    M = mv ... Equation 1

    Where m = mass of the body, v = velocity of the body, M = momentum.

    Making v the subject of the equation,

    v = M/m ... Equation 2

    Given: M = 0.80 kg. m/s, m = 0.145 kg.

    Substituting into equation 2,

    v = 0.8/0.145

    v = 5.52 m/s.

    Using the equation of motion,

    v² = u² + 2gs ... Equation 3.

    Where v = final velocity of the rubber ball, u = initial velocity of the rubber ball, s = distance, g = acceleration due to gravity.

    Given: v = 5.52 m/s, u = 0 m/s, g = 9.81 m/s².

    Substituting into equation 2

    5.52² = 0² + 2 (9.81) s

    30.47 = 19.62s

    s = 30.47/19.62

    s = 1.55 m.

    Thus the ball was dropped from a height of 1.55 m
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