An astronaunt lands on the dwarf planet Eris and decides to perform experiments.

Question

An astronaunt lands on the dwarf planet Eris and decides to perform experiments. One of these experiments is to measure the acceleration due to gravity. He finds that the acceleration due to gravity is constant at 0.8 m/s2. Then he finds a deep crater and wants to know its depth so he fires a rope to the center of the crater. He then slides down the rope without friction and finds that his velocity at the bottom is 63.18 ± 0.33 m/s. Using this information and the fact that the astronaunt has a weight with his suit of 240 N on Mars, find the average depth of the crater.

Explanation / Answer

Velocity of the astronaunt, v = (63.18 ± 0.33) m/s So one of the velocity, v1 = (63.18 + 0.33) m/s = 63.51 m/s another velocity, v2 =  (63.18 - 0.33) m/s = 62.85 m/s From the law of conservation of energy we have        Kinetic energy = Potential energy        (1/2)mv^2 = mgh From the above we have, h = v^2/2g             h1 = v1^2/2g = 205.8 m             h2 = v2^2/2g = 201.5 m So the average depth of the crater = (h1 + h2)/2 = 203.65 m             h2 = v2^2/2g = 201.5 m So the average depth of the crater = (h1 + h2)/2 = 203.65 m

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