A bicycle wheel is 30 inches in diameter.
a. to the nearest revolution, how many times will the wheel turn if the bicycle is ridden for 3 miles.
b. suppose the wheel turns at a constant rate of 2.75 revolutions per second. What is the linear speed in miles per hour of a point on the tire?
For a...
Circumference = (pi)(d) = 30pi in
3 mi = 190,080 in
190,080 / 30pi = 6336 / pi = 2017 revolutions
Not sure about the second part.
Part A
(3miles/1)*(5280ft/1mi)*(12in/1ft)*(1rev/15πin) is appx 4033 revolutions
Part B
(2.75rev/1sec)*(60sec/1min)*(60min/1hr)*(15πin/1rev)*(1ft/12in)*(1mi/5280ft) is appx 7.4 mph
The answers an owl as you at house of jug jug bird y'all finen
Maths is so cool
So this is a sensible answer basically you convert inches into miles which is about 190,080 inches then you do 30 times pie and divide them both
a. To find out how many times the wheel will turn if the bicycle is ridden for 3 miles, we need to first calculate the circumference of the wheel.
The circumference of a circle can be found using the formula:
Circumference = π * diameter
where π is approximately 3.14159.
In this case, the diameter of the wheel is given as 30 inches. Therefore, we can calculate the circumference as:
Circumference = 3.14159 * 30 inches
Next, we need to convert the distance ridden (3 miles) into inches, as the circumference is in inches.
1 mile is equal to 5,280 feet, and 1 foot is equal to 12 inches. So, to convert miles to inches:
3 miles = 3 * 5280 feet = 15840 feet
15840 feet = 15840 * 12 inches = 190,080 inches
Now, we can calculate the number of revolutions by dividing the distance ridden (in inches) by the circumference of the wheel:
Number of revolutions = Distance ridden / Circumference
Number of revolutions = 190,080 inches / Circumference
Now, let's substitute the value of the circumference into the equation:
Number of revolutions = 190,080 inches / (3.14159 * 30 inches)
Using a calculator, we can find the approximate answer to the nearest revolution.
b. To calculate the linear speed in miles per hour of a point on the tire, we need to multiply the rate of revolutions per second by the circumference of the wheel and then convert the result to miles per hour.
First, we calculate the linear speed in inches per second by multiplying the rate of revolutions per second by the circumference:
Linear speed (in inches per second) = Rate of revolutions per second * Circumference
Next, we convert the linear speed from inches per second to miles per hour.
1 mile is equal to 5,280 feet, and 1 foot is equal to 12 inches. Also, there are 60 minutes in an hour and 60 seconds in a minute. Therefore, the conversion factor is:
1 mile = 5,280 feet = 5,280 * 12 inches
1 hour = 60 minutes = 60 * 60 seconds
Using these conversion factors, we can convert the linear speed from inches per second to miles per hour:
Linear speed (in miles per hour) = (Linear speed in inches per second * 1 mile * 1 hour) / (5,280 inches * 60 seconds)
Now, we substitute the linear speed in inches per second into the equation:
Linear speed (in miles per hour) = (Linear speed (in inches per second) * 1 mile * 1 hour) / (5,280 inches * 60 seconds)
Using a calculator, we can find the approximate answer in miles per hour.