At a speed of 15 revolutions per min.,how long will it take a wheel of radius 14 in.,rolling on its edge to travel 440 ft.
one rotation = 2πr = 28π inches
= 28π/12 or 7π/3 ft or appr 7.33 ft
number of rotations to go 440 ft
= 440 ÷ (7π/3) = 1320/(7π) or appr 60.024 rotations
time at 15 rotations per min
= (1320/(7π)) / 15
= 4 minutes
To find the time it takes for the wheel to travel 440 ft, we need to determine the distance covered in one revolution and then divide the total distance by that value.
1. First, let's calculate the circumference of the wheel.
- The formula for the circumference of a circle is C = 2πr, where "C" is the circumference and "r" is the radius of the circle.
- Given the radius is 14 inches, therefore, the circumference of the wheel is C = 2 × π × 14.
2. Next, we need to find the distance covered in one revolution of the wheel.
- Since the circumference of the wheel represents one full revolution, the distance covered in one revolution is equal to the circumference of the wheel.
- From step 1, we know the circumference is 2 × π × 14.
3. Now, we can calculate the time it takes for the wheel to travel 440 ft.
- Divide the total distance (440 ft) by the distance covered in one revolution (from step 2).
- Remember to convert the distance covered in one revolution from inches to feet.
- So, the time in minutes is 440 ft / [(2 × π × 14 in) / 12 in/ft].
- Simplifying further, the time is 440 ft / [(2 × π × 14) / 12] min.
By following these steps, you can calculate the result.
To find out how long it will take for the wheel to travel 440 ft, we need to determine the distance covered in one revolution.
The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * radius
In this case, the radius of the wheel is given as 14 inches, so the circumference would be:
Circumference = 2 * π * 14 inches
Next, we need to convert the units to feet since the distance is given in feet. There are 12 inches in 1 foot, so the conversion factor is:
1 foot = 12 inches
Therefore, the circumference in feet would be:
Circumference = (2 * π * 14 inches) / 12
Now, we can calculate the distance covered in one revolution:
Distance per revolution = Circumference
Given that the wheel is making 15 revolutions per minute, we can multiply the distance per revolution by 15 to find the distance covered in one minute:
Distance per minute = 15 * Distance per revolution
Finally, we can divide the total distance of 440 feet by the distance covered in one minute to find out how long it will take the wheel to travel 440 feet:
Time = 440 feet / Distance per minute
By substituting the values into the formula and performing the calculations, we can find the answer to the question.