Question

Acceleration due to gravity on Mars is about one—third that on Earth. Suppose you throw a ball upward with the same velocity on Mars as on Earth. How would the balls maximum height compare to that on Earth?

Answer 1

The ball would travel 3 times as high.

Explanation:

The equation for finding the displacement (vertical height in this case) of an object with a constant acceleration is:

`v^2 = u^2 -2as`

where `s` is the displacement ,
`u` is the initial velocity ,
`v` is the final velocity ,
and `a` is the acceleration .
For more information about the resoning behind this formula, look here.

We can rearrange this formula to give:

`s = (v^2-u^2)/(2a)`

since we want to know about displacement (height).

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When throwing a ball vertically, the velocity at the top of the throw (when the ball is highest) is 0 , so we can remove the `v^2` part of the equation , as `0^2 = 0`.

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Now we can look at this equation in terms of Earth.

`s_(earth) = (-u^2)/(2a)`

The initial velocity `u` remains constant in both cases, but the acceleration due to gravity on mars is one third the acceleration due to gravity on earth or `1/3a`, so our equation for Mars is:

`s_(mars) = (-u^2)/(2xx 1/3 a)`

This can be rearranged to produce:

`s_(mars) = 3(-u^2)/(2a)`

From this we see that `s_(mars) = 3(s_(earth))`.

Therefore the displacement or height (`s`) on mars is three times that on earth so the ball will travel 3 times as high .