(a) The initial speed of the rock is 19.1 m/s.
(b) The greatest height of the rock as measured from the base of the
cliff is 55.6 m.
(c) i. As the ball is thrown up, its kinetic energy is converted to potential energy.
ii. When then ball reaches the maximum height, its kinetic energy becomes zero and it will have maximum potential energy.
iii. When the rock reaches the base of the cliff, its potential energy becomes zero and it will have maximum kinetic energy.
The initial speed of the rock is determined by applying the principle of conservation of mechanical energy as shown below;
Ui + K.Ei = Uf + K.Ef
mghi + ¹/₂mvi² = mghf + ¹/₂mvf²
(0.37 x 9.8 x 37) + ¹/₂(0.37)vi² = (0.37 x 9.8 x 0) + ¹/₂(0.37 x 33)²
134.16 + 0.185vi² = 0 + 201.47
0.185vi² = 201.47 - 134.16
0.185vi² = 67.31
vi² = 67.31/0.185
vi² = 363.84
vi = √363.84
vi = 19.1 m/s
vf² = vi² - 2gh
0 = vi² - 2gh
2gh = vi²
h = vi²/2g
h = (19.1)²/(2 x 9.8)
h = 18.6 m
The maximum height from the base = 37 m + 18.6 m = 55.6 m
When the ball is thrown up, its kinetic energy is converted to potential energy.
When then ball reaches the maximum height, its kinetic energy becomes zero and it will have maximum potential energy.
When the rock reaches the base of the cliff, its potential energy becomes zero and it will have maximum kinetic energy.
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