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The tallest cliffs ever discovered in our solar system are located on Uranus’s moon Miranda (g=0.0772 m/s^2 ). If you were to drop a rock off of one of these cliffs, it would take 12 minutes to hit the bottom. a. How high is the cliff? b. What is the speed of the rock when it hits the bottom?

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MechEngineer

Answer:

a. 20.01 km

b. 55.584 m/s

Explanation:

Assume there's no air resistance there. We can use the following equation of motion to calculate the distance traveled over t = 12 minutes (12 * 60 = 720 seconds):

[tex]s = gt^2/2 = 0.0772 * 720^2/2 = 20010 m = 20.01 km[/tex]

And the speed with it hits the bottom

[tex]v = at = 0.0772*720 = 55.584 m/s[/tex]

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