Answer:
1) The mass of the skier, m = 51.02 kg
2) At top of the hill, v = 0
3) The velocity of the skier at the 30 m height, v = 37.04 m/s
4) The velocity of the skier at the bottom of the hill, v = 44.27 m/s
Explanation:
Given data,
The initial height of the skier from the ground, h = 100 m
The K.E of skier at 100 m = 0 J
The P.E of the skier at 100 m = 50,000 J
1) The mass of the skier,
m = P.E/ gh
= 50,000/ (9,8 x 100)
= 51.02 kg
2) The velocity of the skier at the top of the hill,
At top of the hill, the K.E = 0,
Hence,
v = 0
3) The velocity of the skier at the 30 m height,
P.E = mgh
= 51.02 x 9.8 x 30
= 14,999.88 J
E = P.E + K.E
K.E = E - P.E
= 50,000 - 14,999.88
= 35000.12 J
v = √(2 K.E/m)
= √(2 x 35000.12 / 51.02)
v = 37.04 m/s
4) The velocity of the skier at the bottom of the hill,
At bottom of the hill, P.E = 0 and K.E is maximum
K.E = 50,000 J
v = √(2 K.E/m)
= √(2 x 50000 / 51.02)
v = 44.27 m/s
