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.
To determine the momentum of the probe after the retrorocket ceases to fire, we need to calculate the change in momentum caused by the retrorocket.
The change in momentum (∆p) can be calculated using the impulse-momentum principle, which states that ∆p is equal to the product of the applied force (F) and the time interval for which it is applied (Δt). Mathematically, it can be written as:
∆p = F * Δt
The force applied by the retrorocket is given as 1.29 x 10^6 N, and the time interval for which it is applied is 9.65 seconds. Plugging these values into the formula, we get:
∆p = (1.29 x 10^6 N) * (9.65 s)
Calculating this, we get:
∆p = 1.24585 x 10^7 N·s
Now, to find the momentum of the probe after the retrorocket ceases to fire, we need to calculate the final momentum by subtracting the change in momentum from the initial momentum.
Given that the initial momentum of the probe is 7.84 x 10^7 kg·m/s, we can write:
Final momentum = Initial momentum - ∆p
Final momentum = 7.84 x 10^7 kg·m/s - 1.24585 x 10^7 N·s
Calculating this, we get:
Final momentum = 6.59415 x 10^7 kg·m/s
Therefore, the momentum of the probe after the retrorocket ceases to fire is 6.59415 x 10^7 kg·m/s.