You are standing on the surface of a small spherical moon whose radius is 6.30 * 10⁴ m and mass of 8.00 * 10¹⁸ kg.An astronaut throws a rock of mass 5.00 kg straight upward with a speed 20.0 m/s.(This Moon is too small to have an atmosphere.)What maximum height above the surface of the Moon will the rock reach?

Question

Quizplus · Accepted Answer

The correct answer is E.The maximum height above the surface of the Moon will the rock reach is 1.52 km.Explanation:The work done by the astronaut on the rock is equal to the change in the rock's kinetic energy.$$W = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$where:* W is the work done* m is the mass of the rock* v_f is the final velocity of the rock* v_i is the initial velocity of the rockThe work done by the astronaut is also equal to the change in the rock's gravitational potential energy.$$W = mgh$$where:* g is the acceleration due to gravity* h is the height above the surface of the MoonSetting the two equations equal to each other, we get:$$\frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2 = mgh$$Solving for h, we get:$$h = \frac{v_f^2 - v_i^2}{2g}$$Plugging in the given values, we get:$$h = \frac{(20.0 \ m/s)^2 - (0 \ m/s)^2}{2(1.62 \ m/s^2)} = 1.52 \ km$$

You Are Standing on the Surface of a Small Spherical