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25 May, 11:53

Determine how much farther a person can jump on the moon as compared to the earth if take off speed and angle are the same

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  1. 25 May, 15:14
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    From Newton's Three Laws of Motion, derived formulas are already conveniently presented for a rectilinear motion at constant acceleration. One of its equations is

    y = (Vf² - Vi²) / 2a, where

    y is the vertical height travelled by the object

    Vf is the final velocity

    Vi is the initial velocity

    a is the acceleration

    Now, when a man jumps, the only force acting on him is gravity pulling him down. When he reaches his maximum height, eventually his velocity will reach zero. So, Vf = 0. Suppose all parameters with subscript 1 refers to man jumping on Earth and those with subscript 2 refers to the man jumping on moon. Since initial velocity and angle is said to be the same, when we find the ratio of x₂/x₁, the terms (Vf²-Vi²) cancels out leaving us with

    x₂/x₁ = a₂/a₁

    It is common knowledge that gravity on Earth is 9.81 m/s². According to literature, the gravity on the moon is 1.62 m/s². Thus,

    x₂/x₁ = a₁/a₂ = 9.81/1.62 = 6

    x₂ = 6x₁

    Therefore, the man jumping on the moon can reach 6 times higher than in Earth.
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