Question

If a shuttle is orbiting a planet at a distance of 40 miles from the center of the planet, and is traveling at a rate of 500 miles per hour, how long to the nearest minute will it take to complete one full orbit?

Answer 1

Answer:

Time taken, t = 30.15 minutes

Explanation:

It is given that,

Distance from the center of planet, r = 40 miles

Speed of the shuttle, v = 500 miles per hour

Let t is the time taken by it to complete  one full orbit. The displacement of the shuttle is,

$d=2\pi r$

$d=2\pi \times 40$

d = 251.32 miles

Now time can be calculated using the expression for the velocity as :

$v=\dfrac{d}{t}$

$t=\dfrac{d}{v}$

$t=\dfrac{251.32\ miles}{500\ miles\ per\ hour}$

t = 0.50264 hours

or

t = 30.15 minutes

So, the shuttle will take 30.15 minutes to complete one full orbit. Hence, this is the required solution.