How to Calculate the Final Speed of a Space Probe?

Question:

What are the steps to calculate the final speed of a space probe based on the given data?

Answer:

The final speed of a space probe can be calculated using the principle of conservation of momentum. By following these steps, you can determine the final speed accurately.

Explanation: To calculate the final speed of a space probe, we need to consider the initial momentum of the probe and the change in momentum due to the force exerted by the retrorockets. Here's how you can calculate the final speed step by step:

1. Calculate Initial Momentum:

The initial momentum of the space probe is the product of its mass and initial velocity. In this case, the mass of the probe is 4.82E+4 kg and the initial speed is 10300 m/s. Therefore, the initial momentum can be calculated as:

Initial Momentum = Mass × Initial Velocity

Initial Momentum = 4.82E+4 kg × 10300 m/s = 4.961E+8 kg·m/s

2. Calculate Change in Momentum:

The change in momentum is due to the force generated by the retrorockets over a certain distance. The force is 4.14E+5 N and the distance is 2480 km (or 2.48E+6 m). Calculate the change in momentum as:

Change in Momentum = Force × Distance

Change in Momentum = 4.14E+5 N × 2.48E+6 m = 1.0252E+12 kg·m/s

3. Calculate Final Speed:

The final speed of the space probe can be determined by subtracting the change in momentum from the initial momentum and dividing by the mass of the probe. Calculate the final speed as:

Final Speed = (Initial Momentum - Change in Momentum) / Mass

Final Speed = (4.961E+8 kg·m/s - 1.0252E+12 kg·m/s) / 4.82E+4 kg = -1.464E+4 m/s

By following these calculations, you can determine the final speed of a space probe accurately. Understanding the principle of conservation of momentum is key to solving such problems effectively.