A 58-kg astronaut is in space, far from any objects that would exert a significa

Question

A 58-kg astronaut is in space, far from any objects that would exert a significant gravitational force on him. He would like to move toward his spaceship, but his jet pack is not functioning. He throws a 720-g socket wrench with a velocity of 5 m/s in a direction away from the ship. After 0.50 s, he throws an 800 g spanner in the same direction with a speed of 8 m/s. After another 9.90 s, he throws a mallet with a speed of 6 m/s in the same direction. The mallet has a mass of 1095 g. How fast is the astronaut moving after he throws the mallet?

Explanation / Answer

mass of astronaut m = 58 kg mass of socket m ' = 720 g = 0.72 kg from law of conservation of momentum , mu = -m' u ' from this velocity of the astronaut after throw the socket u = - m' u ' / m where u ' = velocity of the socket = 5 m / s So, u = -0.062 m / s after 0.5 s : ----------- mass of spanner m " = 800 g = 0.8 kg velocity of spanner u " = 8 m / s from law of conservation of momentum , mu + m" U = mv + m " u" where U = initial speed of spanner = 0            v = velocity of the astronaut after collision mu = mv + m " u "     v = ( mu - m" u " ) / m        = -0.17234 m / s after 9.9 s : ----------- mass of mallet M = 1095 g = 1.095 kg speed of mallet V = 6m / s from law of conservation of momentum , mv = mv ' + MV                     v ' = ( mv - MV ) / m                          = -0.2856 m / s the astronaut speed after he throws the mallet  = 0.2856 m / s

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