Question

Jack Bumblespeed, our fearless space walker, runs out of fuel in his power pack while drifting at 1.0 m/s away from the International Space Station. Jack, remembering what he learned in physics class, removes his 25.0 kg power pack and throws it away at 3.4 m/s relative to the Station and in the direction away from the Station. The mass of Jack plus space suit, minus power pack, is 101.0 kg. Calculate the new relative velocity of Jack towards the Space Station to see if he will catch up with the Station. Take velocity away from the Station to be minus. Tries 0/10

Answer 1

By applying conservation of momentum, Jack's new velocity towards the International Space Station, after throwing the power pack, is calculated to be approximately 0.107 m/s.

Step-by-step explanation:

To calculate the new relative velocity of Jack towards the International Space Station, we need to apply the principle of conservation of momentum. Before throwing the power pack, the total momentum of Jack plus the power pack moving together can be calculated by the sum of their individual momenta. After throwing the power pack, Jack's velocity will change in the opposite direction. To find Jack's new velocity, we use the following equation:

Momentum before = Momentum after

(Mass of Jack + Mass of power pack) × velocity of Jack = (Mass of Jack) × velocity of Jack after + (Mass of power pack) × velocity of power pack

Substituting the given values:

(101.0 kg + 25.0 kg) × (-1.0 m/s) = (101.0 kg) × velocity of Jack after + (25.0 kg) × (-3.4 m/s)

Solving for Jack's velocity after throwing the power pack, we get:

velocity of Jack after = [126.0 kg × (-1.0 m/s) - 25.0 kg × (-3.4 m/s)] / 101.0 kg

velocity of Jack after = (0.107 m/s)
Therefore, Jack will drift toward the International Space Station at a velocity of approximately 0.107 m/s.