Distance a rocket travels on a launch ramp

[clope023]

[SOLVED] Distance a rocket travels on a launch ramp

Homework Statement

A 1600kg rocket is to be launched with an initial upward speed of 51.0m/s . In order to assist its engines, the engineers will start it from rest on a ramp that rises 53 degrees above the horizontal. At the bottom, the ramp turns upward and launches the rocket vertically. The engines provide a constant forward thrust of 2000N , and friction with the ramp surface is a constant 500N .

How far from the base of the ramp should the rocket start, as measured along the surface of the ramp?

Homework Equations

K1 + U1 + Wother = K2 + U2

U1 = mgd(sin53)

K1 = 0

Wother = 2000N-500N = (1500N)d

K2 = 1/2m(51m/s)^2

U2 = 0

The Attempt at a Solution

mgd(sin53) + 1500Nd = 1/2(1600kg)(51m/s)^2

d(mgsin53 + 1500N) = 1/2(1600kg)(51m/s)^2

d = 1/2(1600kg)(51m/s)^2/(mgsin53 + 1500N)

would this be correct?

 

[clope023]

that was the right answer, sorry if I wasted anybody's time...

 

[Moetasim]

Your attempt at a solution looks correct. You have correctly identified all the relevant forces acting on the rocket and used the work-energy theorem to solve for the distance the rocket will travel on the ramp. Additionally, you have correctly taken into account the change in kinetic and potential energy of the rocket as it travels up the ramp. Overall, your solution seems to be a sound and logical approach to solving the problem. Good job!