Question

An astronaut finds herself in a predicament in which she has become untethered from her shuttle. She figures that she could get back to her shuttle by throwing one of three objects she possesses in the opposite direction of the shuttle. The masses of the objects are 5.4 kg, 7.9 kg, and 10.1 kg, respectively. She is able to throw the first object with a speed of 15.00 m/s, the second with a speed of 10.6 m/s, and the third with a speed of 5.5 m/s. If the mass of the astronaut and her remaining gear is 75.0 kg, determine the final speed of the astronaut with respect to the shuttle if she were to throw each object successively, starting with the least massive and ending with the most massive. Assume that the speeds described are those measured in the rest frame of the astronaut.

Answer 1

m1 = mass of first object thrown = 10.1 kg

v1 = velocity with which first object is thrown = 15 m/s

m2 = mass of second object thrown = 7.9 kg

v2 = velocity with second object thrown = 10.6 m/s

m3 = mass of third object thrown = 5.4 kg

v3 = velocity with third object thrown = 5.5 m/s

m = mass of astronaut and her remaining gear = 75 kg

v1i = velocity of astronaut after throwing first object

using conservation of momentum

0 = m1 v1 - (m + m2 + m3) v1i

0 = (10.1) (15) - (75 + 7.9 + 5.4) v1i

v1i = 1.72 m/s

v2i = velocity of astronaut after throwing second object

using conservation of momentum

- (m + m2 + m3) v1i = m2 v2 - (m + m3) v2i

- (75 + 7.9 + 5.4) (1.72) = (7.9) (10.6) - (75 + 5.4) v2i

v2i = 2.93 m/s

v3i = velocity of astronaut after throwing third object

using conservation of momentum

- (m + m3) v2i = m2 v3 - (m) v3i

- (75 + 5.4) (2.93) = (5.4) (5.5) - (75) v3i

v3i = 3.54 m/s

final speed = 3.54 m/s