An 8.5 diameter bowling ball is released at the foul line and starts rolling towards the head pin. If it is 60 feet from the foul line to the headpin, how many revolutions will the ball make before it hits the headpin?
To determine the number of revolutions the ball will make before hitting the headpin, we need to calculate the circumference of the bowling ball, which is given by the formula:
Circumference = π * diameter
The diameter of the bowling ball is 8.5 inches, so we can substitute this value into the formula:
Circumference = π * 8.5 inches
To convert inches to feet, we divide the circumference by 12:
Circumference = (π * 8.5 inches) / 12 = (π/12) * 8.5 inches
The distance from the foul line to the headpin is given as 60 feet. So, to find the number of revolutions the ball will make, we divide the distance by the circumference:
Number of revolutions = 60 feet / (π/12) * 8.5 inches
Now, we need to convert the inches to feet by dividing by 12:
Number of revolutions = 60 feet / ((π/12) * 8.5 inches / 12)
Simplifying the expression inside the parentheses:
Number of revolutions = 60 feet / (π/12) * 8.5/12
Number of revolutions ≈ 12.15
Therefore, the ball will make approximately 12 revolutions before hitting the headpin.