Force/Projectile Motion Problem

[JoshMP]

Homework Statement

Sam (75 kg) takes off up a 50-m-high, 10 degree frictionless slope on his jet-powered skis. The skis have a thrust of 200 N. He keeps his skis tilted at 10 degrees after becoming airborne. How far does Sam land from the base of the cliff?

Homework Equations

F=ma
Kinematic Equations

The Attempt at a Solution

I drew a free body diagram with Thrust pointing ten degrees out and with gravity pointing down. I set (Fnet)x=max, and solved for ax..which I found to be 2.63 m/s^2. I now have the accelerations of Sam along the x and y axes. I don't have v0, s, or t. How do I solve this problem?

 

[Delphi51]

The question isn't clear. Is the ramp 50 m high or 50 m long? Where is the ramp relative to the cliff?

I don't see how you got 2.63 for the acceleration.
It seems to me you have to work out the part while he is on the ramp and the part where he is flying separately.

 

[JoshMP]

The question isn't clear. Is the ramp 50 m high or 50 m long? Where is the ramp relative to the cliff?

I don't see how you got 2.63 for the acceleration.
It seems to me you have to work out the part while he is on the ramp and the part where he is flying separately.

The edge of the ramp is 50 m high. The edge of the ramp *is* the cliff.

I got 2.63 for ax by setting (Fnet)x equal to the x coordinate of Thrust. Thrust=200 N, so Thrust(x)= 200 cos 10=197=m*ax. Ergo ax=2.63 m/s^2.

The part while he is on the ramp cannot be calculated since no distance or initial speed is given. My strategy for solving the problem was to find the x and y accelerations by finding the net forces from the thrust and gravity, then using those x & y accelerations in the kinematic equations and treating the rest as a projectile motion problem, using the moment he leaves the cliff as t=0.

 

[Delphi51]

I would do the ramp part by assuming Vi = 0 and finding the length of the ramp using the 10 degrees and 50 m height. While on the ramp, Fg acts downward and Thrust along the ramp. The ramp also pushes on the guy, cancelling out the part of Fg that is into the ramp. So the only forces are the thrust and the component of Fg that is along the ramp surface.

I haven't thought about the flight part yet. I guess you'll have accelerated motion in both horizontal and vertical directions.