The wheels of a car have a radius of 11 inches and are rotating at 600 revolutions per minute, find the speed of car in mileage per hour.
arrgh, English units :(
r = (11/12) ft
2 pi r = 5.76 ft/revolution
600 revolutions/min * 60 min/hr =36,000 rev/hr
36,000 rev/hr * 5.76 ft/rev = 207,360 ft/hr
207,360 ft/hr * 1 mile/5280 ft
= 39.3 miles/hr
To find the speed of the car in mileage per hour, we first need to find the distance traveled by the car in one minute.
The radius of the car's wheels is given as 11 inches. Since the wheels are rotating, the circumference of each wheel is equal to 2π times the radius.
Circumference = 2π × radius = 2 × 3.14 × 11 inches = 68.64 inches
Now, we need to find the distance traveled by the car in one minute.
Distance traveled in one minute = Circumference of wheel × number of wheel rotations per minute = 68.64 inches × 600 revolutions = 41184 inches
To convert the distance from inches to miles, we divide the distance by 63,360 inches (which is the number of inches in 1 mile).
Distance traveled in one minute in miles = 41184 inches ÷ 63360 inches/mile ≈ 0.649 miles
Since we have determined the distance traveled by the car in one minute, we can now find the speed of the car in mileage per hour by multiplying the distance by 60 (to convert minutes to hours since there are 60 minutes in an hour).
Speed of the car in mileage per hour = Distance traveled in one minute × 60 = 0.649 miles × 60 = 38.94 miles/hour
So, the speed of the car is approximately 38.94 miles per hour.
To find the speed of the car in mileage per hour, we need to convert the wheel's revolution per minute to inches per hour and then convert it to miles per hour. Let's break down the calculations step-by-step:
Step 1: Calculate the circumference of the wheel.
The circumference of a circle can be calculated using the formula: circumference = 2 * π * radius.
Given the radius of the wheel is 11 inches, the circumference would be: 2 * π * 11 = 22π inches.
Step 2: Calculate the distance traveled in inches per minute.
Since the wheel is rotating at 600 revolutions per minute, the distance traveled in inches per minute would be equal to the circumference multiplied by the number of revolutions, i.e., 22π * 600 inches.
Step 3: Convert inches per minute to inches per hour.
To convert inches per minute to inches per hour, multiply the distance traveled in inches per minute by 60 (since there are 60 minutes in an hour). Therefore, the distance traveled in inches per hour would be 22π * 600 * 60 inches.
Step 4: Convert inches per hour to miles per hour.
Since there are 12 inches in a foot and 5280 feet in a mile, divide the distance traveled in inches per hour by (12 * 5280) to get the distance traveled in miles per hour. Thus, the speed of the car in miles per hour would be (22π * 600 * 60) / (12 * 5280) miles per hour.
Now, we can simplify this expression further:
Step 5: Simplify the expression to find the speed in miles per hour.
Converting 22π to a decimal (π ≈ 3.14159), we have:
Speed (in mph) = (22 * 3.14159 * 600 * 60) / (12 * 5280) mph.
Evaluating this expression with a calculator, we find that the speed of the car is approximately 58.94 miles per hour.
Therefore, the speed of the car is approximately 58.94 miles per hour.