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

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°.

Answer 2

Answer:

2.78 radians or 159.36°

Step-by-step 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,

$13in\frac{1ft}{12in}=1.08ft$

Now, we find the angle.

$s=\theta r\\\theta=\frac{3ft}{1.08ft}=2.78 \ rad$

Therefore, the angle is 2.78 radians.

To have it in degrees, we have to transform.

$\pi \ rad =180\°\\2.78 \ rad \frac{180\°}{\pi rad}=\frac{500.4}{3.14}=159.36\°$