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

Time taken, t = 30.15 minutes

Step-by-step 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 * 40`

d = 251.32 miles

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

`v=(d)/(t)`

`t=(d)/(v)`

`t=(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.