Suppose that on earth you can jump straight up a distance of 45 cm Asteroids are made of material with mass density 2800 kg m 3 What is the maximum diameter of a spherical asteroid from which you could escape by jumping

Question: Suppose that on earth you can jump straight up a distance of 45 cm. Asteroids are made of material with mass density 2800 kg/m 3

Suppose that on earth you can jump straight up a distance of 45 cm. Asteroids are made of material with mass density 2800 kg/m³.
What is the maximum diameter of a spherical asteroid from which you could escape by jumping?

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Model Model the asteroid as a spherical mass and yourself as a point mass This is an isolated system so mechanical energy is conserved Visualize The radius of the asteroid is R a and its mass is M a Solve We first calculate your jumping speed on the earth The conservation of energy equation gives The conservation of energy equation U i K i U f K f for the asteroid gives The minimum speed for escape is the one that will cause you to stop only when the separation between you and the asteroid becomes very large Noting that v f 0 ms as r the whole right side is zero Use M a 43R 3 a and rearrange to get Solve for R a The maximum diameter of asteroid you could escape by jumping is twice this radius or 47 km Assess This is a ... View full answer

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