A 200.0 kg astronaut and equipment move with a velocity of 2.00 m/s toward an orbiting spacecraft. How long will the astronaut need to fire a 100.0 N rocket backpack to stop the motion relative to the spacecraft?

Question

100*timefiring= mass*changevelocity

Answer 1

To find the time the astronaut needs to fire the rocket backpack, we first need to find the acceleration caused by the 100 N force. We can use the formula:

Force = mass * acceleration
100 N = 200 kg * acceleration

Now we can solve for acceleration:

acceleration = 100 N / 200 kg
acceleration = 0.5 m/s^2

Next, we can use the formula for acceleration to find the time it takes to come to a stop:

change in velocity = acceleration * time
-2 m/s = 0.5 m/s^2 * time

Now we can solve for time:

time = -2 m/s / 0.5 m/s^2
time = -4 s

However, we cannot have a negative time, so the astronaut should fire the rocket backpack in the opposite direction:

time = 4 s

So the astronaut needs to fire the rocket backpack for 4 seconds to stop the motion relative to the spacecraft.