A new planet which has ten times the mass of the Earth and four times the radius

Question

A new planet which has ten times the mass of the Earth and four times the radius.
a) What is the acceleration due to gravity on this planet?

While on the surface of this planet, an astronaut proceeds to hit a golf ball towards the new planet. The ball has a mass of 0.25 kg on earth, and leaves the ground with a speed of 20 m/s at an angle of 30 degrees up from the horizontal.
b) What is the mass of the golf ball on this planet?
c) What is the wieght of the golf ball on this planet?
d0 How much time will the ball spend in the air before returning to the ground?
e) How far from the astronaut will the ball land?

Explanation / Answer

mass of Earth = M, mass of the planet = 10M,
radius of Earth = R, radius of the planet = 4R
a) the acceleration due to gravity on Earth = g = GM/R2 = 9.8 m/s2

the acceleration due to gravity on the planet = g' = G(10M)/(4R)2 = (10/16)g = 6.13 m/s2

m = 0.25 kg, v = 40 m/s, = 30o,

b) mass m = 0.25 kg

c) weight w = mg' = 1.53 N

d) vertical displacement = vsin*t - g't2/2 = 0

so t = 2vsin/g' = 6.53 s

e) d = vcos*t = 131 m

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