Kang and Kodos orbit the Earth in a spaceship 20,000 km above Springfield.the period of their orbit (hours) is 11.8 and findthe speed (m/s) their spacecraft travels.
b) Speed of spacecraft in meters per second
m/s
.
To find the speed of Kang and Kodos' spacecraft in meters per second, we need to use the formula for the circumference of a circle:
Circumference = 2 * π * r
In this case, the distance from their spaceship to the center of the Earth is given as 20,000 km. To convert this distance to meters, we multiply it by 1000 (since 1 km is equal to 1000 meters):
Distance = 20,000 km * 1000 m/km = 20,000,000 m
Now, let's substitute this value into the formula for the circumference:
Circumference = 2 * π * 20,000,000 m
To find the speed of the spacecraft, we need to divide the circumference by the period (time taken to complete one orbit). The period is given as 11.8 hours. However, we need to convert it to seconds because the speed is measured in meters per second:
Period = 11.8 hours * 60 minutes/hour * 60 seconds/minute = 42,480 seconds
Now, let's calculate the speed:
Speed = Circumference / Period
Speed = (2 * π * 20,000,000 m) / 42,480 s
Using a calculator to evaluate this expression gives us:
Speed ≈ 2980.975 m/s
Therefore, the speed of Kang and Kodos' spacecraft is approximately 2980.975 meters per second.