The Little Prince is a fictional character who lives on a very small planet as shown in the figure below. Suppose that the planet has a mass of 1.95 1013 kg and a radius of 1.06 103 m.

Question

(a) How long would it take for an object to fall from rest a vertical distance of 1.16 m?




(b) Suppose the Little Prince throws a ball vertically upward, giving it an initial velocity of 1.00 m/s. What would be the maximum height reached by the ball? (HINT: Don't assume g to be constant.)

Incorrect: Your answer is incorrect.

Answer 1

1.16 m is tiny compared to the radius of 1.06*10^3 meters so I will assume g is constant for part (a)
m g = G m M/r^2
g = 6.67*10^-11 (1.95*10^13)/(1.06^2*10^6)
= 11.6*10^-4 m/s^2
d = (1/2)gt^2 =1.16

for part (b) the kinetic energy + potential energy at the bottom = potential energy at the top.

(1/2)m v^2 - G mM/r= -GmM/(r+h)

1/2 = GM [1/r - 1/(r+h)]
.5 = (6.67*10^-11)(1.95*10^13)[1/r - 1/(r+h)]

.0384*10^-2 = [1/r - 1/(r+h)]

.0384*10^-2 = 1/1.06*10^3 -1/(1.06*10^3+h)

-.0384*10^-2 + .000943 = 1/(1060+h)

.000559 = 1/(1060+h)
1060+h = 1789
h = 729 meters (huge due to tiny g)