Question

While visiting Planet Physics, you toss a rock straight up at 13.6 m/s and catch it 3.50 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 340.0 minutes. What is the radius (in m) of the planet?

What is the mass (in kg) of the planet?

Answer 1

3.5/2 = 1.75 seconds to peak height
v = Vi - g t
0 = 13.6 - g (1.75) solve for local g on surface. At 2 r it is g/4

340 min = 340 * 60 seconds = T

m * centripetal acceleration = m (g/4) at 2 radii from center

m v^2/2r = = m g/4
v^2/r = g/2
but we know T
v T = 2 pi (2r) = 4 pi r
v = 4 pi r/T
v^2 = 16 pi^2 r^2/T^2
v^2/r = (16 pi^2/T^2) r
so in the end
r = (g/2)/(16 pi^2/T^2)