A 60kg skier with an initial velocity of 12 m/s coasts up a hill. At the top of the hill, the skirt is travelling at 9.75 m/s. Assuming there is no friction in the skis, how high was the hill?
A. 2.5 m
B. 10 m
C. 0.25 m
D. 7.35 m
To solve this problem, we need to use the conservation of mechanical energy. The skier starts with only kinetic energy and ends with both kinetic and potential energy at the top of the hill.
The initial kinetic energy is given by KEi = (1/2)mv^2 = (1/2)(60 kg)(12 m/s)^2 = 4320 J.
At the top of the hill, the skier has potential energy and kinetic energy. The potential energy is given by PE = mgh, where m is the mass of the skier (60 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the hill.
The final kinetic energy is given by KEf = (1/2)mv^2 = (1/2)(60 kg)(9.75 m/s)^2 = 2840.625 J.
Using the conservation of energy, we can set up the equation:
KEi = KEf + PE
4320 J = 2840.625 J + mgh
Simplifying the equation:
4320 J - 2840.625 J = mgh
1479.375 J = mgh
Solving for h:
h = (1479.375 J) / (mg)
Substituting the values:
h = (1479.375 J) / ((60 kg)(9.8 m/s^2))
h = 2.5 m
Therefore, the height of the hill is 2.5 m. The answer is A.