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 determine the momentum of the probe after the retrorocket ceases fire, we can use the formula:
Momentum (p) = mass (m) * velocity (v)
Given data:
Initial momentum (p1) = 7.5e7 Kg*m/s
Force applied by retrorocket (F) = 2.0e6 N
Duration of firing (t) = 12 s
First, let's calculate the initial velocity (v1) of the probe using the momentum formula:
p1 = m * v1
Rearranging the formula, we have:
v1 = p1 / m
Next, let's calculate the change in momentum (∆p) caused by the retrorocket firing:
Force (F) = ∆p / ∆t
Rearranging the formula, we have:
∆p = F * ∆t
Now, let's calculate the final momentum (p2) of the probe:
p2 = p1 - ∆p
Given:
p1 = 7.5e7 Kg*m/s
Now, we need to find the mass (m) of the probe. The mass can be calculated by rearranging the momentum formula:
m = p1 / v1
Finally, we can calculate the change in momentum (∆p) caused by the retrorocket firing:
∆p = F * t
Using the calculated values, we can substitute them back into the formula for the final momentum (p2):
p2 = p1 - ∆p
Let's calculate the values step by step:
1. Calculate initial velocity (v1):
v1 = p1 / m
2. Calculate mass (m) using the initial momentum (p1) and initial velocity (v1):
m = p1 / v1
3. Calculate the change in momentum (∆p) caused by the retrorocket firing:
∆p = F * t
4. Calculate the final momentum (p2):
p2 = p1 - ∆p
By following these steps, we can determine the momentum of the probe after the retrorocket ceases fire.
To determine the momentum of the probe after the retrorocket ceases fire, we can use the principle of impulse-momentum.
The impulse experienced by an object is equal to the change in momentum it undergoes. It can be calculated by multiplying the force applied to the object by the time interval over which the force is applied.
The impulse can be expressed using the equation:
Impulse = force * time
Given that the force applied by the retrorocket is 2.0e6 N and the firing period is 12 s, we can calculate the impulse as:
Impulse = 2.0e6 N * 12 s
Now, according to the principle of impulse-momentum, the change in momentum is equal to the impulse. Therefore, the momentum of the probe after the retrorocket ceases fire is the initial momentum minus the impulse.
Given that the initial momentum of the probe is 7.5e7 kg*m/s, we can calculate the momentum after the retrorocket ceases fire:
Momentum = Initial momentum - Impulse
Substituting the values and calculating:
Momentum = 7.5e7 kg*m/s - (2.0e6 N * 12 s)
Therefore, the momentum of the probe after the retrorocket ceases fire is the calculated value from the equation.