Answer to Question #169036 in Physics for Karma

Question

A model rocket is fired vertically upwards from rest at ground level. The rocket accelerates upwards at 20m/(s^2) for 15 seconds and then runs out of fuel. Air resistance is negligible.

Calculate the rocket's maximum height above the ground as well as the time the rocket is in the air from launch to crashing on the ground.

Answer 1

The maximum height above the ground:

$$h=\frac{at^2}{2}=2250\text{ m}.$$

The total time in air:

$$T=t+t',\\\space\\ t'=\sqrt{\frac{2h}{g}}=21.4\text{ s},\\\space\\ T=15+21.4=36.4\text{ s}.$$