Average speed and average velocity

[mandi182]

Homework Statement

The space shuttle takes off from Cape Canaveral in Florida and orbits Earth 18 times before landing back at Cape Canaveral 23 hours and 7 minutes later. During this time, it moves in circular orbit with radius 6.6 x10^6 m.

Homework Equations

The equation that I am using is Vave=(xfinal-x initial) /(tfinal-t inital)

The Attempt at a Solution

I figured out the circumfrence which is 4.14*10^7 and then I multiplied that by 18 which gives me 7.46*10^8. I subtracted this and it gives me 7.05*10^8. I also converted 23.7 hours into 83220 seconds. I then took 7.05*10^8/83220 and got 8471.2m/s. According to to the book this is incorrect. Can someone tell me what I am doing wrong?

~Thanks

 

[Doc Al]

I figured out the circumfrence which is 4.14*10^7 and then I multiplied that by 18 which gives me 7.46*10^8. I subtracted this and it gives me 7.05*10^8.

Why did you subtract? You want the distance traveled, which is 18 circumferences.

 

[mandi182]

I subtracted because I was using the average velocity formula in my book. Final displacement-Inital displacement/ final time-initial time.

Without subracting, I got 8969.51m/s which is also not the correct answer.

 

[Doc Al]

Is the book answer a bit less? Perhaps they want you to include the distance traveled from Earth to the orbital radius and back.

 

[mandi182]

I think that I have to include the distance but how do I find that?

 

[vela]

You're calculating the average speed, not the average velocity. Which does the problem ask for?

 

[mandi182]

The problem asks for both. I am just not sure how to solve either one.

 

[vela]

OK, do you know the difference between the two?

 

[mandi182]

Average velocity takes into account total displacement and time while speed does not take into account direction.

 

[vela]

Right.

Displacement is just the difference between where you started and where you ended up. So say you leave your house to go to the bank 1 mile away to the north and come back home an hour later. You started at your house and ended up back at your house, so your initial position and final position are the same. The net displacement is therefore 0 miles. (Because the direction matters, the 1 mile you traveled north was canceled out by the 1 mile you traveled south to get back home.) Your average velocity is 0 miles per hour.

On the other hand, to get to the bank and back, you had to travel a total distance of 2 miles. Since you don't care about the direction, the 1 mile you traveled getting to the bank simply adds to the 1 mile you traveled coming back home. Your average speed is 2 miles per hour.

In this problem, so far, you've calculated the distance traveled -- 18 times around the Earth --so you're finding the average speed.

 

[Doc Al]

I think that I have to include the distance but how do I find that?

Compare the radius of the Earth (look it up) with the radius of the orbit.