The question is a child slides down a slide with a 28 degree incline and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of the kinetic friction between the slide and the child.

Answer 1

If the speed is half, the kinetic energy gain is 1/4 of its frictionless value. That means 3/4 of the potential energy loss in moving down the slide a distance X was turned into frictional heat. Frictional heat is work done against the friction force.

(3/4)X M g sin 28 = M g cos28 * mu * X

The M, g and X cancel out. Solve for the coefficient of friction, mu.
mu = (3/4) tan28

Answer 2

.399