The tires on a car are 25 inches in diameter. If the car is moving at a constant speed of 65 miles per hour, how many rotations per second is the front left tire making? Express your answer as a decimal to the nearest tenth. (1 mile = 5280 feet)
distance covered in one rotation
= 25π inches
65 miles/hr
= 65*12*5280 inches/hour
= 65*12*5280/3600 inches/sec
number of rotations
= 65*12*5280/3600 ÷ (25π)
= 14.56.. / sec
or appr 15 rotations per second
check:
distance in 1 second = 14.56*25π
= appr 1143.5 inches
= 4116743.013 inches per hour
= 4116743.013/(12*5280) miles/hr = 64.97
not bad
To find the number of rotations per second the front left tire is making, we can use a few conversion factors.
First, let's convert the speed from miles per hour to feet per second. Since 1 mile is equal to 5280 feet and there are 60 minutes in an hour, we can multiply the speed by the conversion factor:
65 miles/hour × (5280 feet/1 mile) × (1 hour/60 minutes) × (1 minute/60 seconds) = 95.333... feet/second
Next, let's find the circumference of the tire. The circumference of a circle is given by the formula:
Circumference = π × diameter
The diameter of the tire is 25 inches, so the circumference is:
Circumference = π × 25 inches
Now, we need to convert the circumference from inches to feet. Since there are 12 inches in a foot, we can divide the circumference by the conversion factor:
Circumference = (π × 25 inches) ÷ (12 inches/1 foot) = (25/12)π feet
Finally, we can find the number of rotations per second by dividing the speed by the circumference:
Rotations per second = 95.333... feet/second ÷ ((25/12)π feet) = 7.675... rotations/second
Rounded to the nearest tenth, the front left tire is making approximately 7.7 rotations per second.
To find the number of rotations per second that the front left tire is making, we need to determine the distance traveled by the car in one second and divide it by the circumference of the tire.
First, let's convert the speed from miles per hour to inches per second:
65 miles per hour = (65 miles/hour) * (5280 feet/mile) * (12 inches/foot) * (1 hour/3600 seconds)
= (65 * 5280 * 12) / 3600 inches/second
≈ 228.8 inches/second
Next, we need to calculate the circumference of the front left tire. The circumference of a circle can be calculated by the formula:
Circumference = π * diameter
Substituting the given diameter into the formula:
Circumference = π * 25 inches
Since we want the number of rotations per second, we need to divide the distance traveled in one second (228.8 inches) by the circumference of the tire.
Rotation per second = Distance traveled in one second / Circumference of the tire
= 228.8 inches / (π * 25 inches)
Calculating this value:
Rotation per second ≈ 2.9 rotations/second
Therefore, the front left tire is making approximately 2.9 rotations per second.