Question

A baseball is thrown vertically up to a height of 30 m on Earth. If the same ball is thrown up on the moon with the same initial speed, how much farther will it travel up

Answer 1

Answer:

hmax = 181.48m

Explanation:

In order to calculate the maximum height reached by the same ball in the moon, you first calculate the initial velocity of the ball by using the information about the maximum height on the Earth. You use the following formula:

$h_{max}=\frac{v_o^2}{2g}$     (1)

hmax: maximum height reached by the ball in the Earth = 30m

vo: initial velocity of the ball = ?

g: gravitational acceleration on Earth = 9.8m/s^2

From the equation (1) you solve for vo:

$v_o=\sqrt{2gh_{max}}=\sqrt{2(9.8m/s^2)(30m)}=24.24\frac{m}{s}$

Next, you use the same equation (1) but for the gravitational acceleration of the moon, which is given by:

g' = 1.62m/s^2

$h_{max}=\frac{(24.24m/s)^2}{2(1.62m/s^2)}=181.48m$

The same ball, with the same initial velocity, will reache a heigth of 181m in the moon.