Question

An astronaut of mass 60 kg is on a space walk to repair a communications satellite when he realizes he needs to consult the repair manual. You happen to have it with you, so you throw it to him with a speed 4 m/s relative to the spacecraft. He is at rest relative to the spacecraft before catching the 3 kg book. Find (a) his velocity after catching the book (b) the initial and final kinetic energies of the book-astronaut system and (c) the impulse exerted by the book on the astronaut.

Answer 1

a)
Aplly conservation of momentum

m1*u1 + m2*u2 = (m1+m2)*v

v = (m1*u1+m2*u2)/(m1+m2)

= (3*4 + 0 )/(3+60)

= 0.19 m/s

b) KEi = 0.5*m1*u1^2 + 0.5*m2*u2^2

= 0.5*3*4^2 + 0

= 24 J

c) impulse on austronaut = chnage in momentum of the astronaut

= m2*(v2-u2)

= 60*(0.19 - 0)

= 11.4 N.s or kg.m/s

Answer 2

mbUb ma + mb) v

where v is the final velocity, which is hence given by

amy ma + mh

v = 3*4/63 = 4/21 m/s

initial Kinetic energy = 0.5 *3*16 = 24J

final K.E = 0.5 *63 * 16 / 441 = 1.143 J

loss = 22.857 J

Impulse on the man = change in momentum = 60 * 4/ 21 = 11.42 kg m /s

Answer 3