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23 April, 21:04

A parachutist descending at a speed of 15.1 m/s loses a shoe at an altitude of 41.2 m. What is the speed of the shoe just before it hits the ground? The acceleration due to gravity is 9.81 m/s^2. When does the shoe reach the ground? Answer in units of s.

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  1. 24 April, 00:27
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    Speed = 32.19 m/s

    Time = 1.742 seconds

    Explanation:

    Given;

    Initial speed of the shoe i. e the speed of the parachutist = 15.1 m/s

    height above the ground = 41.2 m

    Acceleration due to gravity = 9.81 m/s²

    Now,

    from the Newton's equation of motion

    we have

    v² - u² = 2as

    where,

    v is the final speed

    u is the initial speed

    a is the acceleration = 9.81 m/s² (since it is a case of free fall)

    s is the distance

    thus,

    we have

    v² - 15.1² = 2 * 9.81 * 41.2

    or

    v² = 808.344 + 228.01

    or

    v² = 1036.354

    or

    v = 32.19 m/s

    hence,

    the speed of shoe just before it hits the ground is 32.19 m/s

    also,

    from Newton's equation of motion

    v = u + at

    where, t is the time

    thus,

    32.19 = 15.1 + 9.81 * t

    or

    9.81 * t = 17.09

    or

    t = 1.742 seconds
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