In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track. The combined mass of monkey and sled is 14 kg, and the coefficient of kinetic friction between sled and incline is 0.20. How far up the incline do the monkey and sled move?

Approximately , assuming that .

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

.

Weight of the slide:

.

Normal force between the sled and the slope:

.

Calculate the kinetic friction between the sled and the slope:

.

Assume that the sled and its passenger has reached a height of meters relative to the base of the slope.

Gain in gravitational potential energy:

.

Distance travelled along the slope:

.

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

.

In other words, the sled and its passenger would have lost (approximately) of energy when it is at a height of .

The initial amount of energy that the sled and its passenger possessed was . All that much energy would have been converted when the sled is at its maximum height. Therefore, when is the maximum height of the sled, the following equation would hold.

.

Solve for :

.

.

Therefore, the maximum height that this sled would reach would be approximately .

∠cbe and ∠deb are same-side interior angles.

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