The amount of gravitational potential energy of a Rocket (4U Physics)

Question

2. A 222 kg weather rocket reaches its maximum height 32 km above the Earth's surface. Determine:
a)The amount of gravitational potential energy at its maximum height.
b) Its speed when it hits the ground (neglect frictional effects).

 

I just need the answers to these questions, not sure what the answer is. This is 4u Physics (high school) in Canada. If you need my notes let me know.

Answer 1

(a)

 

r = distance from center of earth

R = radius of earth

h = height above earth

U = gravitational potential energy

M = mass of earth

m = mass of rocket

G = constant of universal gravitation

 

U(r) = -GMm/r = -GMm/(R + h)

 

Plug in h = h_max, and the other numbers.

 

(b)

 

E = total mechanical energy = constant

 

At the ground,

 

h = 0

r = R

 

mv²/2 - GMm/R = E

 

At maximum height, the speed is instantaneously zero, and the potential energy equals the total energy.  Therefore,

 

E = -GMm/(R + h_max) ⇒

 

mv²/2 - GMm/R = -GMm/(R + h_max)

 

Solve for v.

 

v = √{2GM[1/R - 1/(R + h_max)]}

 

Plug in the numbers.