Question

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

Answer 1

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.