1. Understand the Concepts

* Momentum: Momentum (p) is the mass (m) of an object multiplied by its velocity (v): p = mv.

* Impulse: Impulse (J) is the change in momentum of an object. It is also equal to the force (F) applied to the object multiplied by the time (t) over which the force acts: J = F * t.

* Conservation of Momentum: In a closed system, the total momentum before an event is equal to the total momentum after the event.

2. Set up the Problem

* Mass (m): 200 pounds (convert to kilograms: 200 pounds * 0.4536 kg/pound ≈ 90.7 kg)

* Initial Velocity (v): 2 m/s

* Force (F): -100 N (negative because it's acting in the opposite direction of motion)

3. Calculate the Initial Momentum

* p = mv = (90.7 kg)(2 m/s) = 181.4 kg*m/s

4. Calculate the Time to Stop

* Since we want to stop the motion, the final momentum will be 0 kg*m/s.

* The change in momentum (impulse) is: J = 0 kg*m/s - 181.4 kg*m/s = -181.4 kg*m/s

* Using the impulse equation: J = F * t, we can solve for time:

* t = J / F = -181.4 kg*m/s / -100 N = 1.814 seconds

Answer: The astronaut and equipment will need to fire the rocket for approximately 1.814 seconds to stop their motion relative to the spacecraft.