The acceleration due to gravity at the surface of a planet depends on the planet

Question

The acceleration due to gravity at the surface of a planet depends on the planet's mass and size; therefore other planets will have accelerations due to gravity different from 9.8 m/s2. Imagine an astronaut stands on an alien planet, which has no atmosphere, and throws a rock with a speed of 7.35 m/s in the horizontal direction, releasing it at a height of 1.40 m above the surface of the planet. The rock hits the surface a horizontal distance of 8.70 m from the astronaut. Find the magnitude of the acceleration due to gravity on this alien planet. m/s2

Explanation / Answer

We have X = UT = U sqrt(2H/g); so g = (U/X)2 * 2H = (7.35/8.7)2 * 2*1.4 = 1.998 m/s^2

Note Ux = U cos(theta) = U cos(0) = U when thrown "horizontal." And H = 1/2 gT2 is the height dropped during the time of flight T.

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