P02L2019 – Slanted Rocket Launch

Slanted Rocket Launch

A test rocket is launched by accelerating it along an inclined ramp of length $L$ at acceleration $a$, starting from rest at point $A$. The ramp is positioned at an angle $\theta $ above the horizontal. At the instant the rocket leaves the ramp, its engines turn off and it is only under the influence of gravity. You can ignore any air resistance.

1. Find an expression for the velocity of the rocket at the instant it leaves the ramp in terms of $a$ and $L$.

2. Find an expression for the maximum height above the ground reached by the rocket in terms of $a$, $L$, and $\theta $.

3. Let $L=200\ m$, $a=1.25\ m/s^2$, and $\theta =35{}^\circ $. Find how far along the ground from point $A$ the rocket lands.