Angular Distance & Arc Distance: Homework Solution

[Kikki:)]

Homework Statement

The driver of a boat sets the throttle and ties the wheel, making the boat travel at a uniform speed of 12.5m/s in a circle with a diameter of 115m. Through what angular distance does the boat move in 4.00 minutes? What arc distance (in meters) does it travel in this time?

Homework Equations

The Attempt at a Solution

The diameter is 115m, radius is 57.5m, time is 4 min.

But noww is the average velocity 12.5m/s or is 12.5m/s final speed? I know that it is going at constant speed and it does have acceleration. So we take 12.5m/s x 240sec = 3,000m But for the arc distance you take the radius of 57.5 x 2pi(57.5) = 20,763m?

 

[0ddbio]

You are trying to use the instantaneous velocity as if it were an angular quantity.

When working with speeds of things rotating or traveling in circles, what you want is the angular velocity \omega.
So find out how to find what the angular velocity is given the instantaneous velocity.

 

[Kikki:)]

Ohh so their somewhat the same just use it differently. Much thanks! :]