How many times is the maximum height of a body thrown upwards at a speed of 20 m / s greater

| June 21, 2021 | education

How many times is the maximum height of a body thrown upwards at a speed of 20 m / s greater on the moon than on Earth? (acceleration of gravity on the moon 1.6 m / s)

V0 = 20 m / s.

gz = 9.8 m / s2.

gl = 1.6 m / s2.

hl / hz -?

According to the law of conservation of total mechanical energy, the total mechanical energy of a body is conserved.

At the moment of throwing, the total mechanical energy of the body consists only of the kinetic energy Ek = m * V0 ^ 2/2.

At the maximum height, the body stops, the total mechanical energy of the body consists only of the potential energy En = m * g * h.

Ek = En.

m * V0 ^ 2/2 = m * g * h.

The maximum lifting height will be determined by the formula: h = V0 ^ 2/2 * g.

hz = V0 ^ 2/2 * gz.

hl = V0 ^ 2/2 * gl.

hl / hz = V0 ^ 2 * 2 * gz / 2 * gl * V0 ^ 2 = gz / gl.

hl / hz = 9.8 m / s2 / 1.6 m / s2 = 6.125.

Answer: the maximum height of the body’s rise on the Moon will be 6.125 times greater than on Earth hl / hz = 6.125.



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