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Answer to Question #5326 in Mechanics | Relativity for sharif ibrahim

Question #5326
A 100g stone is thrown straight upwards at 19 m/s from the top of a 75 m building.

(a) What is the Stone's velocity as it hits the ground?
(b) What is the maximum height of the stone?
(c)What is the stone's kinetic energy when the gravitational potential energy is 30% less than when it started?
(d) What is the stone's gravitational potential energy 1.0 s before it touches the ground?
Expert's answer
m=100 kg
h=75m
v0=19m/s
a) When the stone hits the ground it`s the gravitational potential energy is equal zero, so let`s use the law of energy conservation:
data:image/png;base64,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
b) The maximum height of the stone is achieved when the stone`s kinetic energy is equal zero. So let`s use the law of energy conservation:
data:image/png;base64,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
c) Let`s use the law of energy conservation:
data:image/png;base64,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
d) We need use the time of the fall
data:image/png;base64,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
Answer:
a) 42.8 m/s
b) 93.4 m
c) 40.1 kj
d) 39.2 kj

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