A space probe is traveling in outer space with a momentum that has a magnitude of 7.84 x 107 kg·m/s. A retrorocket is fired to slow down the probe. It applies a force to the probe that has a magnitude of 1.29 x 106 N and a direction opposite to the probe's motion. It fires for a period of 9.65 s. Determine the momentum of the probe after the retrorocket ceases to fire.

mv = 7.84*10^7

acceleration from the force is
a = F/m = -1.29*10^6/m
so, v after force is

7.84*10^7/m - (1.29*10^6/m)(9.65)
= 6.6*10^7/m

so the final momentum is 6.6*10^7 kg-m/s

sorry about using m for mass as well as meters.

To determine the momentum of the probe after the retrorocket ceases to fire, we need to use the principle of conservation of momentum. According to this principle, the initial momentum of the probe before the retrorocket is equal to its final momentum after the retrorocket has stopped.

The initial momentum of the probe can be calculated using the magnitude given, which is 7.84 x 10^7 kg·m/s.

To find the change in momentum caused by the retrorocket, we need to calculate the impulse applied by the retrorocket. Impulse can be calculated by multiplying the force applied by the retrorocket by the time period for which it applies force. Here, the force applied by the retrorocket is 1.29 x 10^6 N, and the time period is 9.65 s.

Impulse = Force x Time = (1.29 x 10^6 N) x (9.65 s)

Now, the change in momentum is equal to the impulse:

Change in Momentum = Impulse = (1.29 x 10^6 N) x (9.65 s)

To find the final momentum of the probe after the retrorocket ceases to fire, we can subtract the change in momentum from the initial momentum:

Final Momentum = Initial Momentum - Change in Momentum

Now we can substitute the values to calculate the final momentum.

Final Momentum = 7.84 x 10^7 kg·m/s - ((1.29 x 10^6 N) x (9.65 s))

Solving this equation will give you the final momentum of the probe after the retrorocket ceases to fire.