Dynamics and Forces - Conservation of Momentum

Question

After a 1.30 x 10^2kg astronaut (incl. equipment) connects a safety line (length = 22.0m) to herself and to the spacecraft (mass = 2.80 x 10^3kg), she pushes against the craft and moves away at a constant velocity of 9.0m/s. How long does it take the safety line to become tight?

Answer 1

You first need to find out the velocity of the spacecraft using conservation of momentum

 

m₁v_{1 =} m₂v₂

 

(the spacecraft will move off in the opposite direction)

 

then use the kinematic equation 

 

x=vt

 

where v is the separating velocity. (add the two velocities)