automobiles suppose the arm of a windshield wiper is 16 in. long, with a blade 12 in. long. if the wiper moves through an angle of 90, how much of the windshield is cleaned in one pass of the wiper ?
To determine how much of the windshield is cleaned in one pass of the wiper, we need to find the length of the arc swept by the wiper blade.
The length of the arc swept by an object moving through a given angle can be calculated using the formula:
Arc Length = (Angle / 360) * (2 * π * Radius)
In this case, the radius of the wiper arm is 16 inches. Since the wiper moves through an angle of 90 degrees, we can substitute these values into the formula to find the arc length:
Arc Length = (90 / 360) * (2 * π * 16)
Simplifying the calculation:
Arc Length = (0.25) * (2 * π * 16)
Arc Length = 0.5 * (π * 16)
Arc Length = 8π inches
Therefore, the wiper blade will clean an arc length of 8π inches in one pass.