the wheel ( including the tire) of a sports car under development by one of the Big Three auto companies has an 11 in radius. what would be the car's speed in miles per hour if its wheel are turning 800 rpm?
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800 rev/ 1 min x 60 min/ 1 hr x 2 pi radians/ 1 revolution x 11 in / 1 radian x 1 ft/ 12 in x 1 mi/ 5280 ft
= 52.36ft
Did I do this correctly?
52.36 mi / hr
11*2pi in/rev * 800rev/min * 1mi/(5280*12)in * 60min/hr = 52.36mi/hr
You are correct
Yes, you started solving the problem correctly. However, your final calculation seems to be wrong.
To calculate the car's speed in miles per hour, we need to determine the distance the car travels in one hour, given that its wheel is turning at 800 revolutions per minute (rpm) and that the wheel has an 11-inch radius.
Here's a step-by-step calculation:
1. Convert revolutions per minute (rpm) to revolutions per hour (rph):
800 rpm x 60 minutes = 48,000 rph
2. Determine the circumference of the wheel:
Circumference = 2 x π x radius
Circumference = 2 x 3.14 x 11 inches
Circumference = 69.08 inches
3. Convert the circumference from inches to feet:
One foot is equal to 12 inches, so we divide the circumference by 12:
69.08 inches ÷ 12 = 5.76 feet
4. Determine the distance traveled in one revolution:
Since the circumference of the wheel represents the distance traveled in one revolution, it is equal to 5.76 feet.
5. Calculate the distance traveled in one hour:
Distance traveled in one hour = distance per revolution x revolutions per hour
Distance traveled in one hour = 5.76 feet x 48,000 rph
Distance traveled in one hour = 276,480 feet
6. Convert the distance from feet to miles:
One mile is equal to 5,280 feet, so we divide the distance in feet by 5,280:
276,480 feet ÷ 5,280 = 52.36 miles
Therefore, the car's speed, in miles per hour, with the wheel turning at 800 rpm and an 11-inch radius is approximately 52.36 miles per hour.
So, unfortunately, it seems that there was an error in the final calculation you provided. But now you have the correct answer.