Physics
posted by Amy .
I need help with this physics problem: A child slides down a playground slide; the coefficient of kinetic friction is uk=0.25, and angle that the slide makes with the horizontal is 28.0 degree. She begins from rest and slides through a vertical height of 3.5 m. With what speed does she exit the slide?

There are several ways to do this. Let's try conservation of energy. The loss of potential coming down (M g H)is equal to the gain in kinetic energy, (1/2) M V^2, PLUS work done against friction while sliding. The length of the slide is H/sin 28 = 7.46m, where H = 3.5 m is the vertical height. The friction force is M g cos28*uk. The friction work done is therefore
W = M g (H/sin 28)* cos28 *uk
= M g uk/tan28
M g H = M g H uk/tan 28 + (1/2)M V^2
Note that the M's cancel. That's good, because they did not tell you what the mass was.
V^2 = 2 g H [1  uk/tan28]