Question

Starting from rest a model rocket accelerates upwards at 24 m/s. How long does it take to reach a height of 192 meters

Answer 1

Answer:

$t=4s$

Explanation:

We want to write the equation of displacement (vertical in this case) for accelerated motion, which is $y=y_0+v_yt+\frac{a_yt^2}{2}$. If we take the upward direction as positive, assume it starts from rest and from the ground, and $a_y=24m/s^2$ (the units are wrong in the text, if accelerates at that magnitude, it's an acceleration, in particular in $m/s^2$), then we have $y=(12m/s^2)t^2$.

We want to know the time when $y=192m$, so we need to solve $192m=(12m/s^2)t^2$, for which we have:

$t=\sqrt{\frac{192m}{12m/s^2}}=4s$

This means it takes 4 seconds for a rocket accelerating at $24m/s^2$ to reach a height of 192m.