15. The height achieved in a jump is determined by the initial vertical velocity that the jumper is able to achieve. Assuming that this is a ﬁxed number, how high can an athlete jump on Mars if she can clear 1.55 In on Earth?
22. The radius of a neutron star is T50 times smaller than Earth's radius, and its mass is 1.8 H 105 times larger than Earth's mass. What is the escape velocity from the surface of a neutron star? (Ignore the fact that, at ((high speeds, one should not really use mv^2/2 for the kinetic energy.)
52. Rather than a tunnel through Earth's center, consider a tunnel drilled along a chord of Earth, meaning
that it passes a perpendicular distance d away from the center of Earth (attached). Find the potential energy of a mass placed in such a tunnel as a function of (a) its distance r from the center of Earth and (b) its distance x from the midpoint of the tunnel.
57. A binary star system consists of two stars, each of mass M, orbiting around their common center of mass with radii R from the center of mass. Determine the period of revolution.
Calculations involving gravitational forces on the Earth and different planets.