A 48.0-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 0.720-kg socket wrench with a velocity of 5.00 m/s in a direction away from the ship. After 0.500 s, he throws a 0.800-kg spanner in the same direction with a speed of 8.00 m/s. After another 9.90 s, he throws a mallet with a speed of 6.00 m/s in the same direction. The mallet has a mass of 1.20 kg. How fast is the astronaut moving after he throws the mallet?(assume all speeds are relative to the spaceship). m/s

The astronaut is moving at a speed of 0.36m/s

Explanation:

Speed here corresponds to velocity

The astronaut's mass = 48kg

velocity of astronaut = ?

mass of socket = 0.72kg

velocity of socket = 5m/s

mass of the spanner = 0.8kg

velocity of spanner = 8m/s

change in time = 0.05 -0 = 0.05sec

mass of the mallet = 1.2kg

velocity of mallet = 6m/s

change in time = 9.9 -0 = 9.9sec

To find the astronaut velocity, we would calculate the total momentum which is the astronaut.

∑momentum (M) = ∑astronaut momentum

∑M = ∑astronaut M

∑astronaut M = M of socket + M of spanner + M of mallet

momentum = mass × velocity

(mass × velocity)of astronaut = (0.72×5) + (0.8×8) + (1.2×6)

48 × velocity of astronaut= 3.6 + 6.4 + 7.2

48 × velocity of astronaut= 17.2

velocity of astronaut = 17.2/48

velocity of astronaut = 0.36m/s

The astronaut is moving at a speed of 0.36m/s

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