A 5.50 104 kg space probe is traveling at a speed of 11000 m/s through deep space. Retrorockets are fired along the line of motion to reduce the probe's speed. The retrorockets generate a force of 4.00 105 N over a distance of 2600 km. What is the final speed of the probe?

The decrease in momentum, M*(V1 - V2)

is equal to the retrorocket thrust force times the time.

Solve for V2.

it doesn't give me the time...

To find the final speed of the space probe, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the net force acting on the space probe is provided by the retrorockets, and we can calculate the acceleration using the formula:

Force = Mass × Acceleration

Rearranging the formula to solve for acceleration:

Acceleration = Force / Mass

Now, we have the force exerted by the retrorockets, which is 4.00 × 10^5 N, and we also have the mass of the space probe, which is 5.50 × 10^4 kg. We can plug in these values to find the acceleration:

Acceleration = (4.00 × 10^5 N) / (5.50 × 10^4 kg)

Now, we can calculate the acceleration:

Acceleration ≈ 7.27 m/s²

Next, we can use the formula for acceleration to find the change in velocity (Δv):

Δv = Initial Velocity - Final Velocity

Since the retrorockets reduce the speed of the space probe, the initial velocity is 11000 m/s. We need to find the final velocity, so the formula can be rearranged as:

Final Velocity = Initial Velocity - Δv

We know the acceleration (Δv) is 7.27 m/s² and the initial velocity is 11000 m/s. Plugging in these values, we can calculate the change in velocity:

Δv = 7.27 m/s²

Final Velocity = 11000 m/s - 7.27 m/s²

Now, we can calculate the final velocity:

Final Velocity ≈ 10992.73 m/s

Therefore, the final speed of the space probe is approximately 10992.73 m/s.