Question

How many times higher could an astronaut jump on the Moon than on Earth if his takeoff speed is the same in both locations (gravitational acceleration on the Moon is about 1/6 of g on Earth)?

Answer 1

Answer:

maximum height on moon is 6 times more than the maximum height on Earth

Explanation:

Let the Astronaut has its maximum speed by which he can jump is "v"

now for the maximum height that it can jump is given as

$v_f^2 - v_i^2 = 2 aH$

now from above equation we will have

$0 - v^2 = 2(-g)H$

now we have

$H = \frac{v^2}{2g}$

now if Astronaut jump on the surface of moon with same speed

then we know that the acceleration of gravity on surface of moon is 1/6 times the gravity on earth

so at surface of moon we have

$0 - v^2 = 2(-g/6) H$

now we have

$H = \frac{6v^2}{2g}$

so maximum height on moon is 6 times more than the maximum height on Earth