## Contents

A foam rocket launcher consists of a compressed spring attached to a platform of mass $$m_p$$, which when released collides with a stationary rocket setting it into motion.

A simplified cross-sectional view of the launch module is shown above.

$$x_0 = {{params.x0}} \ \rm{m}$$, $$x_1 = {{params.x1}} \ \rm{m}$$, $$m_p = {{params.mp}} \ \rm{kg}$$, $$m_r = {{params.mr}} \ \rm{kg}$$, $$k = {{params.k}}$$.

## Part 1#

If the spring is un-deformed at the point of impact $$x_0$$, determine the speed $$u_p$$ of the platform just before it hits the rocket.
Neglect the mass of the spring and any resistive forces. Assume the launcher is fixed to the ground.

Please enter in a numeric value in $$\rm{m/s}$$.

## Part 2#

If the coefficient of restitution between the two colliding surfaces is $$e = {{params.e}}$$, calculate the final speeds of both the rocket and the platform.
Neglect the effects of gravity and force in the spring during the duration of impact.
What is $$v_p$$?

Please enter in a numeric value in $$\rm{m/s}$$.

## Part 3#

What is $$v_r$$?

Please enter in a numeric value in $$\rm{m/s}$$.