A satellite is orbiting the Earth in a circular orbit. It orbits the Earth 3 complete revolutions every 24 hours. How many radians does it travel in 19 hours?

i think its 19pi radians or 19/2pi radians
im kinda conufsed about what i did..need help

displacement= 19/24 (3)*2PI

Note that in 24 hours it travels 3*2PI rad.

set it up as a simple ratio

3 revs = 6pi radians (1 rotation is 2pi)

so 6pi/24 = x/19
x = 19(6pi)/24
x = 19pi/4

you kinda lost me ...can you explain more :]

ok i get it now..thnks

To determine the number of radians that a satellite travels in a given time period, you need to calculate its angular velocity and then multiply it by the time period.

First, we need to find the angular velocity of the satellite. The total number of revolutions in 24 hours is 3, so we can calculate the angular velocity using the formula:

Angular velocity = (Total number of revolutions * 2π) / Total time

In this case, the total number of revolutions is 3 and the total time is 24 hours. Let's substitute these values into the formula:

Angular velocity = (3 * 2π) / 24

Simplifying the equation:

Angular velocity = π / 4

Now that we have the angular velocity, we can proceed to calculate the radians traveled by the satellite in 19 hours.

The formula to calculate the radians traveled is:

Radians = Angular velocity * Time

Substituting the values:

Radians = (π / 4) * 19

Simplifying the equation:

Radians = 19π / 4

So, the correct answer is 19π / 4 radians.