To determine the time it takes for the rocket to reach its maximum height, we can use the following kinematic equation:
\[
v = u + at
\]
where:
- \( v \) = final velocity (0 m/s at the maximum height),
- \( u \) = initial velocity (23.5 m/s),
- \( a \) = acceleration (which will be \(-9.81 \, \text{m/s}^2\) due to gravity acting downward),
- \( t \) = time (what we want to find).
At maximum height, the final velocity \( v \) is 0, so we set up