a car wheel has a 13-inch radius. Through what angle does the wheel turn when the car rolls forward 3 ft?
Accepted Solution
A:
Answer:158.7°
Step-by-step explanation:Data:
r = 13 in
s = 3 ft
Calculations:
(a) Convert feet to inches
s = 3 ft × (12 in/1 ft) = 36 in
(b) Calculate the angle
Let θ = the angle subtended by the arc.
s = rθ
θ = s/r = 36/13 ≈ 2.7692 rad
Convert radians to degrees
2.7692 rad × (360°/2π rad) = 158.7°
The wheel travels through an arc of 158.7°.