SOLUTION: A vehicle has tires that are 75 cm in diameter. Determine the measure of the angle (in radians) through which the point turns every second if the vehicle is travelling at 110 km/h

Question 1102780: A vehicle has tires that are 75 cm in diameter. Determine the measure of the angle (in radians) through which the point turns every second if the vehicle is travelling at 110 km/h
Found 2 solutions by Boreal, solver91311:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
110 km/h=110000m/3600 sec=30.56 m/sec or 3055.56 cm/sec
circumference (2 pi) of wheel is pi*D=75*pi cm
This is 12.968 revolutions per second.
multiply that by 2 pi radians per revolution
81.48 radians per second.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

There are 100 centimeters in a meter and 1000 meters in a kilometer, so there are 100,000 centimeters in a kilometer.

The diameter of the tire is 75 cm, so the circumference of the tire is centimeters.

Hence the number of revolutions of the tire when the car has gone 1 kilometer is .

Since the car is traveling at 110 km/hr, the number of revolutions in an hour is

But there are 60 times 60 or 3600 seconds in an hour, so the number of revolutions per second is:

Since there are radians in 1 revolution, the radian measure of the angle traversed by a point on the tire not located at the center of the tire would be:

You can do your own arithmetic.

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS
A vehicle has tires that are 75 cm in diameter. A point is marked on the edge of the... (answered by josmiceli,Theo)
Story Problem A special vehicle for traveling on glacial ice has tires that are 4.8 ft (answered by robertb)
A special vehicle for traveling on glacial ice has tires that are 4.8 ft in diameter. If (answered by lwsshak3)
Recall that there are 2π radians in one full rotation and 360 degrees in one full... (answered by MathLover1)
n a stretch of interstate, a vehicle's tires rotate at a rate of 840 revolutions per... (answered by ankor@dixie-net.com)
A bicycle has a front wheel with a diameter of 35 cm and a back wheel with a diameter of... (answered by fractalier)
1. Convert 220 degree to radians. Express the angele to 2 decimal places. 2. Estimate... (answered by Alan3354)
A tire on a car has an outside diameter of 37.0837.08 in. Through what angle (in... (answered by fractalier)
A central angle intercepts an arc on a circle equal in length to the diameter of a... (answered by josmiceli)