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30 May, 07:31

5. An object is released from rest on a planet that has no atmosphere. The object falls freely for 3.0 meters in the first second. What is the magnitude of the acceleration due to gravity on the planet? l. 5 m/s^23.0 m/s^26.0 m/s^210.0 m/s^212.0 m/s^2

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  1. 30 May, 07:57
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    the acceleration due to gravity is g = 6 m/s² (option C)

    Explanation:

    if we ignore air friction, the height h an object falls under a gravity g is calculated through:

    h = h₀ + v₀*t - 1/2*g*t²

    where

    t = time to reach a height h

    v₀ = initial vertical velocity of the object = 0 m/s (since is released from rest)

    g = gravity

    h₀ = initial height = 3m

    if the object starts at height h₀ = 3 m then it finishes at height h = 0 m when it falls 3 meters.

    then since v₀=0 m/s:

    h = h₀ - 1/2*g*t²

    replacing values

    0 = 3 m - 1/2*g * (1 s) ²

    g = 2 * (3m - 0m) / (1 s) ² = 6 m/s²

    g = 6 m/s² (option C)
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