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

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.

If football was tossed in air without gravity or friction the ball would go into space

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