Final answer:
The wheel turns through an angle of 360 degrees.
Step-by-step explanation:
To find the angle through which the car wheel turns when the car rolls forward 1 ft, we can use the relationship between linear distance and angular displacement.
The linear distance traveled by the car is 1 ft, which is equal to the circumference of the circle traced by the wheel.
The circumference of the circle can be calculated using the formula C = 2πr, where r is the radius of the wheel. Plugging in the values, we get C = 2π(15 in) = 30π in.
Now, we can find the angle by converting the linear distance to an angular displacement. Since 1 revolution is equal to 360 degrees, we can set up the following proportion:
1 revolution = 360 degrees = 30π inches = x degrees, where x is the angle we want to find. Solving for x, we get x = (360 degrees)(30π inches) / (30π inches) = 360 degrees.
Therefore, the wheel turns through an angle of 360 degrees.