Question

a car wheel has a 13-inch radius. Through what angle does the wheel turn when the car rolls forward 3 ft?

Answer 1

2.78 radians or 159.36°

Explanation:

Givens:

`r=13in`

`\theta =?`

`s=3 ft`

`s` refers to the length of the circumference, which is the same distance rolled.

So, to find the angle, we have to use this definition:

`s=\theta r`; which is the relation between arc, angle and length.

Before, replacing all values, we have to transform 13 inches in feet. We know that 1 feet is 12 inches. So,

`13in(1ft)/(12in)=1.08ft`

Now, we find the angle.

`s=\theta r\\\theta=(3ft)/(1.08ft)=2.78 \ rad`

Therefore, the angle is 2.78 radians.

To have it in degrees, we have to transform.

`\pi \ rad =180\°\\2.78 \ rad (180\°)/(\pi rad)=(500.4)/(3.14)=159.36\°`

Answer 2

158.7°

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°.