Question Text#

At time $t$ = 0 $s$, a large soccer ball is kicked straight up into the air with an initial velocity $\overrightarrow{v_0}$. 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 $\overrightarrow{a}$. 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:

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.