A block of mass 4kg is dropped from a height of 2 meters on Earth. If...

A block of mass 4kg is dropped from a height of 2 meters on Earth. If that block is taken to a different planet, where the acceleration due to gravity is 1/4 as strong as it is on Earth, how high should the block be dropped so that it hits the ground with the same final velocity as on Earth? (Hint: you do not need to use gravitational force for this) Express your answer to a maximum of 2 significant digits.

Solutions

Expert Solution

Mass of the block = 4 kg

Gravitational acceleration on Earth = g₁

Initial velocity of the block as it is dropped on Earth = V₁ = 0 m/s

Final velocity of the block as it reaches the ground on Earth = V₂

Height from which the block was dropped on Earth = H₁ = 2 m

Gravitational acceleration of the other planet = g₂ = g₁/4 = 0.25g₁

Initial velocity of the block as it is dropped on the other planet = V₃ = 0 m/s

Final velocity of the block as it reaches the ground on the other planet = V₄

The final velocity of the block on Earth and the other planet is same.

V₄ = V₂

Height from which the block was dropped on the other planet = H₂

H₂ = 8 m

Height from which the block is dropped on the other planet to have the same final velocity as on Earth = 8 m

genius_generous answered 1 year ago

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