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 6.55 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 9.30 m from the astronaut. Find the magnitude of the acceleration due to gravity on this alien planet. 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 6.55 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 9.30 m from the astronaut. Find the magnitude of the acceleration due to gravity on this alien planet.

Explanation / Answer

speed = U = 6.55 m/s

distance = X = 9.30 m

height = H= 1.40 m

We have X = UT = U sqrt(2H/g);

so g = (U/X)^2 2H =( 6.55/9.30)^2 * 2*1.4 = 1.388 m/s^2 ANS.

Note Ux = U cos(theta) = U cos(0) = U

when thrown "horizontal." And H = 1/2 gT^2 is the height dropped during the time of flight T.

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