# trigonometry

posted by .

A race car is driven around a circular tract at a constant speed of 180 miles per hour. If the diameter of the track is 1/2 miles, what is the angular speed of the car? Express your answer in revolutions per hour.

I know the answer is 114.59 revolutions per hour, but I don't know what steps to take to get to that answer. Please show me.

Thanks.

the arclength a of a circle is given by a=rθ where θ is in radians.

differentiate with respect to t
da/dt = .25dθ/dt
180 = .25dθ/dt
dθ/dt = 720 radians per hour

one revolution is 2pi radians, so divide 720 by 2pi to get 114.59 revolutions.

## Similar Questions

1. ### math

ANGULAR SPEED OF A RACE CAR. A race car is driven around a circular track at a constant speed of 180miles per hour. If the diameter of the track is 1/2mile, what is the angular speed of the car?
2. ### Trigonometry

A race car is driven around a circular track at a constant speed of 180mph. If the diameter is 1/2 mile, what is the angular speed of the car?
3. ### Trigonometry

A race car is driven around a circular track at a constant speed of 180mph. If the diameter is 1/2 mile, what is the angular speed of the car?
4. ### physics

A race car starts from rest on a circular track. The car increases its speed at a constant rate at as it goes 2.75 times around the track. Find the angle that the total acceleration of the car makes with the radius connecting the center …
5. ### Physics

A car can be driven around a 120 m radius curve at constant speed without sliding if the maximum centripetal acceleration is 0.130g. (a) What is the maximum speed that the car can travel around the curve without sliding?
6. ### Math

Two cars run at constant speeds around a one-mile racetrack. If the cars circle the track in the same direction, the faster car passes the slower car every 10 minutes. If the cars circle the track in opposite directions, the cars meet …
7. ### PHY SCI

A race car goes around a circular, level track with a diameter of 1.00 km at a constant speed of 90.0 km/h. What is the car's centripetal acceleration in m/s^2?
8. ### pyscics

a race car starts from rest on a circular track the car in races as its speed at a constant rate of as it goes 2.75 times around the track.find the angle that the total acceleration of the car makes with the radius connecting the centre …
9. ### physics

a race car starts from rest on a circular track.the car increases its speed at constant rate at as it goes 2.75 times around the track.find the angle that the total acceleration of the car makes with the radius connecting the centre …
10. ### Math

The tires on a car are 25 inches in diameter. If the car is moving at a constant speed of 65 miles per hour, how many rotations per second is the front left tire making?

More Similar Questions