Word problems ? Very difficult!?

Question

1. From the known mass and radius of a planet (2.5 x 10^30kg and 8.9x10^7 km), compute the value of the acceleration due to the gravity at the surface of this planet.

2. What is the acceleration due to the gravity 7500m above sea level.

3. How far above Earth´s surface would a 70-kg man have to go to "lose" 15% of this weight ?

Answer 1

1.  

m = 2.5E30 kg

r = 8.9E7 km = 8.9E10 m

G = 6.67E-11 m^3/(kg*s^2)

a = - m*G/r^2

a = -(2.5E30)*(6.67E-11) / (8.9E10)^2

a = -0.021 m/s^2

2.

m = 5.97E24 kg

r = 6.38E6 m (at equator) + 7500 = 6.3875E6 m

G = 6.67E-11 m^3/(kg*s^2)

a = - m*G/r^2

a = -(5.97E24*6.67E-11)/(6.3875E6)^2

a = -9.76

3.

a(r = 6.38E6 + h) = 0.85*a(r = 6.38E6)

a(r = 6.38E6 + h) = 0.85*-(5.97E24*6.67E-11) / (6.3875E6)^2

a(r = 6.38E6 + h) = -8.315

-8.315 = -(5.97E24*6.67E-11)/(6.38E6 + h)^2

h = height = 54.0 km

Answer 2

donno!!