An automobile is traveling at 65 mph. If each tire has a radius of 15 inches, at which rate are the tires spinning in revolutions per minute (rpm)? (63360in=1 mile)
i did
65 miles=1 hour
63360 in=1 mile
1 hour= 60 minutes
1 rev=30 pi
in the end after multiplying i got 728.3 rpm, is this correct?
First, we need to convert the speed from miles per hour to inches per minute. Since 1 mile is equal to 63360 inches, we can calculate the speed in inches per minute as follows:
65 mph * 63360 inches/mile = 4,118,400 inches/minute
Next, we need to find the circumference of the tire to determine the distance traveled per revolution. The circumference can be calculated using the formula:
Circumference = 2 * π * radius
Substituting the given radius of 15 inches into the formula:
Circumference = 2 * 3.14159 * 15 inches = 94.2488 inches
To find the rate at which the tires are spinning in revolutions per minute, we can divide the speed in inches per minute by the distance traveled per revolution:
Rate = Speed / Circumference
Rate = 4,118,400 inches/minute / 94.2488 inches/revolution
Rate ≈ 43,734 revolutions/minute
Therefore, the tires are spinning at approximately 43,734 revolutions per minute.
To find the rate at which the tires are spinning in revolutions per minute (rpm), we can use the following steps:
1. First, let's convert the speed of the automobile from miles per hour to inches per minute. We know that 1 mile is equal to 63,360 inches.
Speed in inches per minute = 65 mph * 63,360 inches/mile
Speed in inches per minute = 4,121,600 inches/minute
2. Now that we have the speed in inches per minute, we can calculate the distance traveled by the tire in one minute. The distance traveled by a tire in one revolution is equal to its circumference, which can be calculated using the formula: circumference = 2 * pi * radius.
Circumference = 2 * 3.14 * 15 inches
Circumference = 94.2 inches
Distance traveled by the tire in one minute = Circumference * Speed in inches per minute
Distance traveled by the tire in one minute = 94.2 inches/rev * 4,121,600 inches/minute
3. Finally, we can find the rate at which the tires are spinning in revolutions per minute (rpm) by dividing the distance traveled in one minute by the circumference of the tire:
Tire Spinning Rate (rpm) = Distance traveled in one minute / Circumference
Tire Spinning Rate (rpm) = 4,121,600 inches/minute / 94.2 inches/rev
Tire Spinning Rate (rpm) ≈ 43,769.95 rpm
Therefore, the rate at which the tires are spinning is approximately 43,770 revolutions per minute.
One rotation = 30π inches, you had that
65 miles per hour
= 65(63360) inches per 60 minutes
= 68640 inches/min
number of rotations = 68640/(30π)
= 728.3 rotations
correct!!!