Question

A 6565 kg rocket is being launched up. It is at rest on the launch pad when the rocket engine starts and supplies a thrust of 125,000 N. How fast will the rocket be traveling after 25 sec?

Answer 1

According to the Newton's second law, the acceleration $a$ of the rocket is:

$$ma = F-mg\\ a = \dfrac{F}{m} -g$$

where $m = 6565 kg$, $F = 125000N$ and $g = 9.81m/s^2$ is the gravitational acceleration.

The distance traveled under the constant acceleration during the time $t = 25s$ is:

$$d = \dfrac{at^2}{2} = \dfrac{t^2}{2}\left (\dfrac{F}{m} -g\right)\\ d = \dfrac{25^2}{2}\left (\dfrac{125000}{6565} -9.81\right)\approx 2884.5 m$$

Answer. 2884.5 m.