Question

A 300,000 kg- spacecraft is floating in space when it senses a 40-kg enemy missile coming toward it at 20m/s. The spacecraft fires at 60 kg lump of clay at 30m/s directly at the missile. The clay sticks to the missile. (a.) Show that the spacecraft recoils at about 6mm/s (1mm=0.001m) (b.) Show that the final velocity of the clay-laden missile is 10 m/s in a direction away from the spacecraft.

Answer 1

Part A: In inelastic collision, Using momentum conservation for clay-spacecraft system

Pi = Pf

M*U = m1v1 + m2v2

M = mass of spacecraft +clay = 300000 kg

m1 = mass of spacecraft = 300000 kg - 60 kg = 299940 kg, and

m2 = mass of clay = 60 kg

U = 0 m/sec = initial velocity of spacecraft + clay

v1 = ? m/sec = final velocity of spacecraft

v2 = 30 m/sec = final velocity of clay

Using these values:

300000*0 = 299940*v1 + 60*30

v1 = -60*30/299940 = -0.00600 m/sec (-ve sign means recoil speed)

v1 = recoil speed of spacecraft = 0.00600 m/sec = 6.00*10^-3 m/sec = 6.00 mm/sec

Part B. In inelastic collision, Using momentum conservation for clay-missile system

m1v1 + m2v2 = (m1 + m2)*V

m1 = mass of clay = 60 kg

m2 = mass of missile = 40 kg

v1 = 30 m/sec = initial velocity of clay

v2 = -20 m/sec = initial velocity of missile (since missile is traveling opposite direction of clay)

V = final velocity of Coupled missile and clay = ?

V = (m1v1 + m2v2)/(m1 + m2)

V = (60*30 + 40*(-20))/(60 + 40)

V = 10 m/sec

(since answer is positive which means final speed is in initial direction of clay, which is traveling away from spacecraft)

Please Upvote.