A wheel with a radius of 13 rolls along level ground and makes 4 1/2 revolutions per second. Assuming the circumference to be 3.1416 times the diameter, how far does the wheel travel in 8 seconds?
distance= circumference*number rotations
= 3.1416*(2*13)*4.5*8
3.1416*(2*13)*4.5*8
To find how far the wheel travels in 8 seconds, we need to calculate the distance covered in one revolution and multiply it by the number of revolutions made in 8 seconds.
First, let's find the circumference of the wheel. We are given that the circumference is 3.1416 times the diameter. The diameter of the wheel is twice the radius, so:
Diameter = 2 * Radius = 2 * 13 = 26 units
Now we can calculate the circumference of the wheel:
Circumference = π * Diameter = 3.1416 * 26 ≈ 81.68 units
Next, let's find the distance covered in one revolution by using the circumference formula: Distance = Circumference.
Distance covered in one revolution = 81.68 units
Since the wheel makes 4 1/2 revolutions per second, we need to calculate the distance covered in one second:
Distance covered in one second = 4.5 * Distance covered in one revolution
Distance covered in one second = 4.5 * 81.68 ≈ 367.56 units
Finally, to find the distance covered in 8 seconds, we multiply the distance covered in one second by 8:
Distance covered in 8 seconds = Distance covered in one second * 8
Distance covered in 8 seconds = 367.56 * 8 ≈ 2940.48 units
Therefore, the wheel travels approximately 2940.48 units in 8 seconds.