Two astronauts, A and B, both with mass of 60kg, are moving along a straight line in the same direction in a "weightless" spaceship. Relative to the spaceship the speed of A is 2 m/s and that of B is

Question

Two astronauts, A and B, both with mass of 60kg, are moving along a straight line in the same direction in a "weightless" spaceship. Relative to the spaceship the speed of A is 2 m/s and that of B is 1 m/s. A is carrying a bag of mass 5 kg with him. To avoid collision with B, A throws the bag with a speed v relative to the spaceship towards B and B catches it. Find the minimum value of v.

TestHub · Accepted Answer

A throws the bag: 65 × 2 = 60 v A ​ + 5 v ⇒ v A ​ = 60 130 − 5 v ​ . B catches it: 60 × 1 + 5 v = 65 v B ​ ⇒ v B ​ = 65 60 + 5 v ​ . No collision needs v A ​ ≤ v B ​ : 65 ( 130 − 5 v ) ≤ 60 ( 60 + 5 v ) ⇒ v ≥ 7.76 ≈ 7.8 m / s . Answer: (A)

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