A spacecraft is orbiting the Earth with a constant speed of 8100 ms . The radtus of its orbit is 6750 km . a Explain what is meant by the term constant speed. b Calculate how far it will travel in 1.0 hour. c Calculate how long it will take to complete one orbit of the Earth. Give your answer in minutes.

Certainly! Let's tackle each part of your question step by step. --- ### **Given:** - **Speed of spacecraft (\( v \))**: 8100 meters per second (m/s) - **Radius of orbit (\( r \))**: 6750 kilometers (km) --- ### **Part a:** Explain what is meant by the term **constant speed**. **Constant speed** means that the spacecraft is moving at a **steady rate** without any acceleration or deceleration. In other words, the magnitude of its velocity remains unchanged over time. This implies: - **Uniform Motion:** The spacecraft covers equal distances in equal intervals of time. - **No Acceleration:** There are no changes in the speed; the spacecraft isn't speeding up or slowing down. - **Straight-Line vs. Circular Motion:** While the spacecraft is in orbit (which is a circular path), **constant speed** refers only to the magnitude of the velocity, not its direction. Even though the direction of the velocity changes continuously as the spacecraft orbits, the speed (magnitude) remains the same. **Key Point:** In the context of orbital motion, **constant speed** ensures that the spacecraft maintains a stable orbit, balancing gravitational pull with its inertia. --- ### **Part b:** Calculate how far it will travel in **1.0 hour**. To find the distance traveled over a certain time when speed is constant, use the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] **Given:** - Speed (\( v \)) = 8100 m/s - Time (\( t \)) = 1.0 hour **Convert Time to Seconds:** \[ 1 \text{ hour} = 60 \text{ minutes} = 60 \times 60 = 3600 \text{ seconds} \] **Calculate Distance:** \[ \text{Distance} = 8100 \, \text{m/s} \times 3600 \, \text{s} = 29,160,000 \, \text{meters} \] **Convert to Kilometers (optional):** \[ 29,160,000 \, \text{meters} = 29,160 \, \text{kilometers} \quad (\text{since } 1 \, \text{km} = 1000 \, \text{m}) \] **Answer:** The spacecraft will travel **29,160 kilometers** in **1.0 hour**. --- ### **Part c:** Calculate how long it will take to complete one orbit of the Earth. Give your answer in **minutes**. To determine the orbital period (time to complete one orbit), you can use the formula: \[ \text{Orbital Period} (T) = \frac{\text{Circumference of Orbit}}{\text{Speed}} \] **First, calculate the Circumference (\( C \)) of the orbit:** \[ C = 2\pi r \] **Convert Radius to Meters:** \[ r = 6750 \, \text{km} = 6,750,000 \, \text{meters} \] **Calculate Circumference:** \[ C = 2 \times \pi \times 6,750,000 \, \text{m} \approx 42,411,500 \, \text{meters} \] *(Using \( \pi \approx 3.1416 \))* **Calculate Orbital Period (in seconds):** \[ T = \frac{42,411,500 \, \text{m}}{8100 \, \text{m/s}} \approx 5238.9 \, \text{seconds} \] **Convert Seconds to Minutes:** \[ 5238.9 \, \text{s} \div 60 \approx 87.315 \, \text{minutes} \] **Rounding:** \[ T \approx 87.3 \, \text{minutes} \] **Answer:** It will take approximately **87.3 minutes** for the spacecraft to complete one orbit around the Earth. --- ### **Summary of Answers:** - **a.** Constant speed means the spacecraft moves at a steady rate without speeding up or slowing down. - **b.** In 1.0 hour, the spacecraft travels **29,160 kilometers**. - **c.** The orbital period is approximately **87.3 minutes**. If you have any further questions or need additional clarification, feel free to ask!