Answer :
Final answer:
The linear velocity of the tip of the lawnmower blade spinning at 3000 RPM in a lawnmower that cuts a 26-inch wide path is approximately (26π/31680) miles per hour.
Explanation:
To find the linear velocity of the tip of the lawnmower blade, we need to convert the revolutions per minute (RPM) to inches per minute first. The circumference of the circle created by the spinning blade can be calculated using the formula C = 2πr, where r is the radius of the circle. Since the blade cuts a path that is 26 inches wide, the radius would be half of that, which is 13 inches. Therefore, the circumference is 2π(13) = 26π inches per revolution. We can then find the linear velocity by multiplying the circumference by the number of revolutions per minute, and then converting the units from inches per minute to miles per hour.
First, let's convert the units from inches per minute to miles per hour. There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour. So, 26π inches per minute would be:
(26π inches/minute) × (1 foot/12 inches) × (1 mile/5280 feet) × (60 minutes/hour) = (26π/31680) miles per hour.
Therefore, the linear velocity of the tip of the lawnmower blade spinning at 3000 RPM in a lawnmower that cuts a 26-inch wide path is approximately (26π/31680) miles per hour.
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