A car is traveling at 40 mph. The radius of its wheels are 14 inches. How many revolutions per minute?
Please show work. I don't understand this.
change 40mph to inches/minute.
Then, revs= speed/(2PI*r)
What is the Pl?
so 42,240/(2 x Pl*14)
PI (π) is the ratio of the circumference to the diameter of a circle. So, there are 2π*14 = 28π inches in the circumference of the tire -- that's how far the car goes in one revolution of the tires.
Now it's just a matter of converting mi/hr to rev/min
40mi/hr * 1hr/60min * (5280*12)in/mi * 1rev/28πin = 480 rev/min
To determine the number of revolutions per minute, we need to understand the relationship between the car's speed, the radius of its wheels, and the number of revolutions made in a specific amount of time.
First, we need to convert the car's speed from miles per hour to inches per minute since the radius of the wheels is given in inches. To do this, we need to account for the fact that there are 5280 feet in a mile, 12 inches in a foot, and 60 minutes in an hour:
40 mph * (5280 ft/mile) * (12 inches/ft) * (1 hour/60 minutes)
= (40 * 5280 * 12) inches/minute
Next, we need to find the circumference of the wheel to determine how far the car travels in one revolution. The circumference of a circle can be found using the formula: C = 2 * π * r, where C is the circumference and r is the radius.
Given that the radius of the car's wheels is 14 inches, we have:
C = 2 * π * 14 inches
Now, we can calculate the number of revolutions per minute. Since the car travels the circumference of the wheel in one revolution, we can divide the distance traveled in inches per minute by the circumference of the wheel:
(40 * 5280 * 12) inches/minute ÷ (2 * π * 14 inches)
= (40 * 5280 * 12) ÷ (2 * 3.14 * 14) revolutions/minute
Simplifying this expression will give us the final answer, which represents the number of revolutions per minute.