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

1109m

Step-by-step explanation:

The distance h₁ traveled by the rocket during acceleration:

`h_1=(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=(1)/(2)mv_1^2+mgh_1=mgh_2`

Solving for h₂:

`h_2=(v_1^2)/(2g)+h_1=((at)^2)/(2g)+(1)/(2)at^2`