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.

 

[nlightner]

I would like to point out that there are a few assumptions made in this solution. First, it is assumed that the rocket is starting from rest and that the engines provide a constant forward thrust throughout the entire launch. Additionally, the friction force is assumed to be constant and the ramp is assumed to be frictionless after the rocket launches vertically. These assumptions may not accurately reflect real-world conditions and could affect the accuracy of the solution. It would be important for engineers to consider these factors and make adjustments accordingly in order to ensure the success and safety of the rocket launch.