Question

A rocket accelerates at 25m/s^2 for 5s before it runs out of fuel and dies. What is the maximum height reached by the rocket?

Answer 1

Answer:

1109m

Explanation:

The distance h₁ traveled by the rocket during acceleration:

$h_1=\frac{1}{2}at^2$

The velocity v₁ at this height h₁:

$v_1=at$

When the rocket runs out of fuel, energy is conserved:

$E=\frac{1}{2}mv_1^2+mgh_1=mgh_2$

Solving for h₂:

$h_2=\frac{v_1^2}{2g}+h_1=\frac{(at)^2}{2g}+\frac{1}{2}at^2$