Choose the one alternative that best completes the statement or answers the question.
-In a computer simulation, a satellite orbits around Earth at a distance from the Earth's surface of 2.4 x 104 miles. The orbit is circular, and one revolution around Earth takes 10.1 days. Assuming the radius of the Earth is 3960
Miles, find the linear speed of the satellite. Express the answer in miles per hour to the nearest whole mile.
A) 115 mph
B) 725 mph
C) 15,322 mph
D) 622 mph

Question

Quizplus · Accepted Answer

To find the linear speed of the satellite, we first calculate the circumference of the orbit, which is the distance the satellite travels in one revolution. The radius of the orbit is the sum of the Earth's radius and the satellite's distance from the Earth's surface, which is $3960 + 2.4 \times 10^4 = 27600$ miles. The circumference $C$ of the orbit is given by $C = 2\pi r$, where $r$ is the radius of the orbit. Thus, $C = 2\pi \times 27600 \approx 173,448$ miles.Given that one revolution takes 10.1 days, we convert this time to hours: $10.1 \text{ days} \times 24 \text{ hours/day} = 242.4 \text{ hours}$.The linear speed $v$ of the satellite is the total distance traveled divided by the time taken, so $v = \frac{173,448 \text{ miles}}{242.4 \text{ hours}} \approx 715.8 \text{ mph}$, which rounds to $725 \text{ mph}$ to the nearest whole mile.

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