A 60 kg skier with an initial velocity of 12 m/s coasts up a hill. At the top of the hill, the skier is traveling at 9.75 m/s. Assuming there is no friction in the skis, how high was the hill?
2.5 m%0D%0A2.5 m%0D%0A%0D%0A10 m%0D%0A10 m%0D%0A%0D%0A7.35 m%0D%0A7.35 m%0D%0A%0D%0A0.25 m
To solve this problem, we can use the conservation of energy principle.
The initial kinetic energy of the skier is given by 1/2 * mass * (initial velocity)^2:
KE_initial = 1/2 * 60 kg * (12 m/s)^2 = 4320 J
At the top of the hill, the kinetic energy of the skier is given by 1/2 * mass * (final velocity)^2:
KE_final = 1/2 * 60 kg * (9.75 m/s)^2 = 2849.0625 J
The difference in potential energy between the initial and final positions is equal to the work done against gravity:
ΔPE = m * g * h
Since there is no friction, all the work done is against gravity, so ΔPE = KE_initial - KE_final:
m * g * h = 4320 J - 2849.0625 J
Substituting the values, we find:
60 kg * 9.8 m/s^2 * h = 4320 J - 2849.0625 J
h = (4320 J - 2849.0625 J) / (60 kg * 9.8 m/s^2) = 2.5 m
Therefore, the height of the hill is 2.5 meters.