Final answer:
The tack is approximately 13 inches above the ground after the wheel has traveled 1200 inches, as the wheel's radius is 13 inches and the tack has moved slightly less than three-quarters of a revolution.
Step-by-step explanation:
The question concerns the calculation of the position of a tack that got stuck in a bicycle wheel and the wheel's subsequent movement. Devon's bike has wheels that are 26 inches in diameter. This means the radius of the wheel is 13 inches as the radius is half of the diameter. After the wheel picks up a tack, Devon rolls another 100 feet or 1200 inches before stopping.
To find out how far above the ground the tack is, we need to consider the circular motion of the wheel and the distance Devon traveled. Since the circumference of a wheel is equal to π times the diameter (C = πd), we can calculate the circumference of Devon's bike wheel:
C = π × 26 inches = 81.68 inches.
Next, we need to calculate how many complete revolutions the wheel made in 1200 inches by dividing 1200 by the circumference:
Number of revolutions = 1200 inches / 81.68 inches per revolution ≈ 14.69 revolutions.
Since 14 complete revolutions would leave the tack at the bottom, the extra 0.69 of a revolution would mean it finishes partway through its next cycle. To find out where the tack ends up, we calculate:
0.69 × Circumference = 0.69 × 81.68 inches ≈ 56.36 inches.
This tells us the distance covered by the wheel during the partial revolution after the last complete revolution. Because 56.36 inches is more than half the circumference, we can infer that the tack has passed the topmost point of the wheel and is now on its way down. As the circumference of the wheel is 81.68 inches and the wheel made a little less than three-quarters of a revolution (because three-quarters would be 0.75), the tack is now close to being opposite its starting point.
Therefore, the tack is approximately 13 inches above the ground, which corresponds to the radius of the wheel, since the diameter (and hence the highest point the tack can be) is 26 inches, and the lowest point is 0 inches. The correct answer is A) 13 inches.