A 68.5 kg astronaut is doing a repair in space on the orbiting space station. He throws a 2.25 kg tool with a speed of 3.20 m / s relative to the space station. With what speed and direction will the astronaut begin to move?

Explanation:

Momentum is conserved.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Initially, both the astronaut and the tool are at rest, so u₁ = u₂ = 0 m/s.

After throwing the tool, the tool has a velocity of v₂ = 3.20 m/s.

(68.5 kg) (0 m/s) + (2.25 kg) (0 m/s) = (68.5 kg) v + (2.25 kg) (3.20 m/s)

0 = (68.5 kg) v + 7.2 kg m/s

v = -0.105 m/s

The astronaut moves at a speed of 0.105 m/s in the opposite direction.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach