Rocket Sled (2-D Motion)

Part 1: Find the trajectory (y as a function of x) of the rocket

Part 2: Do as GOAL

A 500g model rocket on a cart is moving horizontally to the right when it is fired with a thrust of 15 N. The goal is to have the rocket pass through a small hoop htat is 2 m to the right of and 20 above the launch point.

What speed does the cart have so that the rocket goes through the hoop? (Hint: Draw a free body diagram.)