Question

The ceiling of a school gymnasium is a distance of 20m. You toss a ball 1.5m from the ground. What is the maximum initial velocity you can toss the ball and have it just miss the ceiling?

Answer 1

In order to determine the maximum initial velocity, use the following formula for the maximum height that an object reaches:

$h=\frac{v^2_o}{2g}$

where,

vo: maximum intial velocity = ?

g: gravitational acceleration constant = 9.8 m/s^2

h: maximum height = 20 m - 1.5 m = 18.5 m

Look that h has been taken regarding with where the ball was thrown.

Solve for vo in the previous formula and replace the values of the oher parameters, as follow:

$v_o=\sqrt[]{2gh}=\sqrt[]{2(9.8\frac{m}{s^2})(18.5)}\approx19.04\frac{m}{s}$

Hence, the maximum initial velocity should be approximately 19.04 m/s