Answer:
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 .