Energy conservation answer check

[Jack21222]

Homework Statement

A 1500kg rocket is to be launched with an initial upward velocity of 50m/s. In order to assist its engines, engineers will start it from rest on a ramp that rises 53 degrees from the horizontal. At the bottom, the ramp turns upward and launches the rocket vertically. The engines provide a constant forward thrust of 2000 N, and friction with the ramp is a constant 500 N. How far from the base of the ramp should the rocket start, as measured along the surface of the ramp?

Homework Equations

E₀ +W_in = E_f + E_lost
U = mgh
KE = 1/2 m v²

The Attempt at a Solution

I need to find the displacement along the ramp. I made the change in x the surface of the ramp, and I made h equal x*sin 53.

Solving for x, I got 141.6m.

 

[Doc Al]

Looks good.