A 66 kg astronaut is in space, far from any objects that would exert a significa

Question

A 66 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 610 g socket wrench with a velocity of 4.6 m/s in a direction away from the ship. After 0.52 s, he throws a 950 g spanner in the same direction with a speed of 8.6 m/s. After another 8.1 s, he throws a mallet with a speed of 6.5 m/s in the same direction. The mallet has a mass of 1, 300 g. How fast is the astronaut moving after he throws the mallet? v_A = m/s

Explanation / Answer

ma = mass of astronaut = 66 kg

ms = mass of socket = 610 g = 0.61 kg

Ms = mass of spanner = 950 g = 0.95 kg

m = mass of malle = 1.3 kg

Case 1 : Astronaut initially at rest and throws socket

assuming towards the ship direction as positive

Vs = velocity of socket away from ship = - 4.6 m/s

V1 = velocity of astronaut after throwing socket = ?

V = initial velocity of astronaut before throwing socket = 0 m/s

using conservation of momentum

(ma + ms + Ms + m) V = ms Vs + (ma + Ms + m) V1

(ma + ms + Ms + m) (0) = (0.61) (- 4.6) + (66 + 0.95 + 1.3) V1

V1 = 0.041 m/s

Case 2 :

Vs = velocity of spanner away from ship = - 8.6 m/s

V1 = velocity of astronaut after throwing socket = 0.041

V2 = velocity of astronaut after throwing spanner = ?

using conservation of momentum

(ma + Ms + m) V1 = Ms Vs + (ma + m) V2

(66 + 0.95 + 1.3) (0.041) = (0.95) (- 8.6) + (66 + 1.3) V2

V2 = 0.163 m/s

Case 3 :

Vm = velocity of mallet away from ship = - 6.5 m/s

V1 = velocity of astronaut after throwing spanner = 0.163 m/s

V2 = velocity of astronaut after throwing mallet = ?

using conservation of momentum

(ma + m) V1 = m Vs + (ma ) V2

(66 + 1.3) (0.163) = (1.3) (- 6.5) + (66) V2

V2 = 0.294 m/s

hence Va = 0.294 m/s

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