
Laura B. answered 10/22/21
Stress Free Studies! Math Tutor with MEd. UCSD, BS Physics UCSC
Hi! Please watch the video for full details, but essentially to solve this problem you need to split it up into two equal parts--the time going up and the time falling back down from the maximum height.
You also need to assume that the rocket goes straight up and down, is being accelerated by gravity on Earth's surface, and launches from the ground. Once you assume all that you have enough information to solve using the time only in your distance and velocity equations.
The reason that this split-up is important is that at maximum height, you can consider the velocity of the rocket to be zero, and this allows you to backsolve to the initial conditions.
I'm sure you can do it! Please watch the video.