Question

Monroe is tracking the circular path of a satellite in the sky using his telescope. He determined that the satellite has formed an arc of 32° in one hour. The satellite is 36,000 km above the earth's surface. How far did the satellite travel in the one-hour period to the nearest kilometer?

Answer Choices:
1) 1,400 km
2) 10,053 km
3)20,106 km
4)72,382 km

Answer 1

To calculate the distance traveled by the satellite, we need to find the circumference of the circle it traces in the sky. The circumference can be found using the formula:

C = 2 * π * r

where r is the radius of the circle (i.e., the distance from the center of the earth to the satellite), and π is pi, approximately equal to 3.14.

r = 36,000 km

C = 2 * π * 36,000 km

C = 72,000 * π km

Next, we need to find what fraction of the circumference the satellite has traveled in one hour. This is given by the fraction of the total circle the satellite has traced, which is equal to the angle it has formed divided by 360°.

fraction = 32° / 360°

Finally, we can multiply the circumference by the fraction to find the distance traveled by the satellite:

distance = C * fraction

distance = 72,000 * π * 32° / 360° km

Rounding the result to the nearest kilometer, the satellite has traveled approximately:

distance = 73,382 km

So, the satellite traveled approximately 73,382 km in one hour.