Question

A baseball pitcher can throw a fastball at 150 km/hr (94 mph). What is the radius of the largest spherical asteroid, density 3 g cm-3 , from which he can throw a ball fast enough that the ball: a. Escapes from the asteroid and goes into heliocentric orbit. b. Goes into circular orbit just above the surface of the asteroid. c. Rises to an altitude of 50 km and falls back.

Answer 1

v = 150 km/hr ~ 42 m/s
rho = 3 g/cm^3 = 3000 kg/m^3

M = rho*V
V = 4/3*pi*r^3

(a) make KE = PE and solve for r, which i get r = v*sqrt(3/8*pi*rho*G) = 32439 m

(b) make Fc = Fg and solve for r, which i get r = v*sqrt(23/4*pi*rho*G) = 45876 m

(c)For part (c) you should use the equation PE=mgh (where m is the mass of the object, g is the gravitational force on the object, and h is the height of the object) You know what the initial kinetic energy is, and that at the peak of the throw; the potential energy will be equal to the the initial potential energy.