# Kicked Soccer Ball#

## Question Text#

At time $$t$$ = 0 $$s$$, a large soccer ball is kicked straight up into the air with an initial velocity $$\vec{v_0}$$. Also at $$t$$ = 0 $$s$$, a small rocket fires its engines such that it is launched straight up into the air with a constant acceleration $$\vec{a}$$. The rocket starts from rest. As shown in the figure, at $$t$$ = 0 $$s$$ the centres of the soccer ball and rocket have the same position.

At what time (other than $$t$$ = 0), do the centres of the soccer ball and rocket once again have the same position? Give your answer in terms of $$v_0$$, $$a$$, and $$g$$. Ignore air resistance.

Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:

For

Use

$$v_0$$

v_0

$$a$$

a

$$g$$

g