A space probe is traveling in outer space with a momentum that has a magnitude of 7.5e7 Kg*m/s. A retrorocket is fired to slow down the probe. It applies a force to the probe that has a magnitude of 2.0e6N and a direction opposite to the probe's motion. It fires for a period of 12s. Determine the momentum of the probe after the retrorocket ceases fire.
To solve this problem, we need to use the concept of impulse and apply it to the given information.
Impulse is defined as the change in momentum of an object. It can be calculated using the formula:
Impulse = Force * Time
In this case, the impulse experienced by the space probe is equal to the change in its momentum.
Given:
Initial momentum of the probe = 7.5e7 kg*m/s (magnitude)
Force applied by retrorocket = -2.0e6 N (opposite to the probe's motion)
Time for which the force is applied = 12 s
Now, let's calculate the impulse experienced by the probe:
Impulse = Force * Time
Impulse = (-2.0e6 N) * (12 s)
To find the change in momentum, we need to express the impulse in terms of momentum:
Impulse = Change in momentum
Therefore,
Change in momentum = (-2.0e6 N) * (12 s)
Now, we know that momentum is a vector quantity and has both magnitude and direction. The given magnitude of momentum is 7.5e7 kg*m/s, but we need to determine its final magnitude.
To do this, we can use the principle of conservation of momentum. According to this principle, the total momentum before and after an event remains constant, assuming no external forces act on the system.
So, we can write the equation:
Initial momentum + Change in momentum = Final momentum
Let's substitute the values:
7.5e7 kg*m/s + (-2.0e6 N) * (12 s) = Final momentum
Now, we can calculate the final momentum by solving the equation:
Final momentum = 7.5e7 kg*m/s + (-2.0e6 N) * (12 s)