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Consider a stone in free fall on a planet with gravitational acceleration 3.4 m/s^2. Suppose you would like the stone to experience the same magnitude of acceleration down an inclined plane on Earth. Neglecting friction and air resistance, which angle should the inclined plane have with respect to the horizontal ? (in deg)

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nuhulawal20

Answer:

Angle of incline is 20.2978Ā°

Explanation:

Given that;

Gravitational acceleration on a planet a = 3.4 m/sĀ²

Gravitational acceleration on Earth g = 9.8 m/sĀ²

Angle of incline = āˆ…

Mass of the stone = m

Force on the stone along the incline will be;

F = mgSināˆ…

F = ma

The stone has the same acceleration as that of the gravitational acceleration on the planet.

so

ma = mgSināˆ…

a = gSināˆ…

Sināˆ… = a / g

we substitute

Sināˆ… = (3.4 m/sĀ²) / (9.8 m/sĀ²)

Sināˆ… = 0.3469

āˆ… = Sinā»Ā¹( 0.3469 )

āˆ… = 20.2978Ā°

Therefore, Angle of incline is 20.2978Ā°

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