Conservative Forces and Friction

[MarineBio]

Homework Statement

A 1.50 kg toy rollercoaster rests on a ramp of height h. When the toy rollercoaster is released, it slides without friction to the bottom of the ramp, and then continues on a flat surface with a rough patch of width 10.0 cm that has a coefficient of kinetic friction µk = 0.770. Find h such that the toy rollercoaster's speed after crossing the rough patch is 3.50 m/s.

Homework Equations

K = 1/2mv^2
U = mgh

The Attempt at a Solution

Kf = 1/2mv^2 = 1/2(1.5kg)(3.5 m/s)^2
Kf = 9.188

fk = ukN = .77(mg) = 11.319 (multiplied by the distance of .1m = 1.132)

I can't do mgh because I don't know h. I know I probably need to figure out how fast the toy roller coaster was going right before it hit the rough patch, but I can't seem to figure that out without knowing "h" so I am stuck here with no idea where to go.

 

[rl.bhat]

Change in KE is equal to work down against rough surface. So Ki = Kf + fk*d
And Ki = mgh.
Find h

 

[MarineBio]

Ahh, brilliant. Thank you so much!