(a) Asteroids have average densities of about 2500 kg/m3 and radii from 470 km down to less than a kilometer. Assuming that the asteroid has a spherically symmetric mass distribution estimate the radius of the largest asteroid from which you could escape simply by jumping off. (Hint: You can estimate your jump speed by relating it to the maximum height that you can jump on earth.) (b) Europa, one of Jupiter’s four large moons, has a radius of 1570 km. The acceleration due to gravity at its surface is 1.33 m/s2. Calculate its average density.

Solution 54P Step 1 a) suppose, the maximum height an average person can jump from the surface of the earth, h = 1 m 2 2 So, we can write, v = u - 2gh on earth At a height h = 1 m , v = 0 m/s 0 = u - (2×9.8 m/s × 1 m) u = 4.43 m/s Initial speed of the person, u = 4.43 m/s