Question

A small asteroid that has a mass of 
120 kg is moving at 225 m/s when it is 1000 km above the Moon.

(a) How fast will the meteorite be traveling when it impacts the lunar surface if it is heading straight toward the center of the Moon? The radius of the Moon is 

1.737 ✕ 106 m.

 m/s

(b) How much work does the Moon do in stopping the asteroid if neither the Moon nor the asteroid heat up in the process?
 J

Answer 1

m = mass of asterroid = 120 kg

M = mass of moon = 7.35 x 10²² kg

V_i = initial speed of asteroid = 225 m/s

r_i = distance between moon and asteroid = radius of moon + height above = 1.737 x 10⁶ + 10⁶ = 2.737 x 10⁶ m

r_f = final distance between moon and asteroid = radius of moon = 1.737 x 10⁶ m

Using conservation of energy ::

KE_i + GPE_i = KE_f + GPE_f       

KE = kinetic energy , GPE = gravitational potential energy

(0.5) mV_i² + (-GmM/r_i )= (0.5) mV_f² + (-GmM/r_f )

(0.5)(225)² - (6.67 x 10^-11) (7.35 x 10²² )/( 2.737 x 10⁶) = (0.5) V_f² - (6.67 x 10^-11) (7.35 x 10²² )/( 1.737 x 10⁶)

V_f = 1453.62 m/s

b)

work done by moon = kinetic energy of asteroid = (0.5) mV_f² = (0.5)(120)(1453.62)² = 1.27 x 10⁸