The driver's side windshield wiper is 75 cm long and spans an angle of 130 degrees in one swipe of the windshield. determine the distance that the tip of the windshield wiper travels in one swipe from left to right across the windshield.
If the wiper were allowed to do a complete rotation it would cover
2(75)π cm
but only does 130/360 part of that
so find (130/360)(150π) cm =
A more interesting question would be:
given that the actual blade of the 75 cm wiper is 40 cm long,
what is the area wiped by the blade in one wipe?
Thank you! It definitely would be a more interesting question!
To determine the distance that the tip of the windshield wiper travels in one swipe from left to right across the windshield, you can use the formula for the arc length of a circle.
Arc Length = (θ/360) * 2 * π * r
Where:
θ = angle in degrees
r = radius of the circle
Given that the driver's side windshield wiper spans an angle of 130 degrees and has a length of 75 cm, let's calculate the distance traveled by the tip.
First, convert the angle to radians:
θ_radians = (130 * π) / 180
θ_radians ≈ 2.2689 radians
Next, substitute the values into the formula:
Arc Length = (2.2689/360) * 2 * π * 75
Simplifying the equation, we get:
Arc Length ≈ (0.0063) * 2 * 3.14 * 75
Arc Length ≈ 0.0126 * 3.14 * 75
Arc Length ≈ 2.9835 cm
Therefore, the tip of the windshield wiper travels approximately 2.9835 cm in one swipe from left to right across the windshield.
To determine the distance that the tip of the windshield wiper travels in one swipe from left to right across the windshield, we need to consider the length of the wiper blade and the angle it sweeps.
Let's break down the problem:
1. Convert the angle from degrees to radians: Since most trigonometric functions use radians, we need to convert the given angle from degrees to radians. To convert degrees to radians, we use the formula: radians = (π / 180) * degrees. For this problem, the given angle is 130 degrees, so the angle in radians is (π / 180) * 130 = 2.2689 radians.
2. Calculate the distance: The distance traveled by the tip of the windshield wiper can be found using the formula for the arc length of a circle. The formula for arc length is arc length = radius * angle in radians. Since the windshield wiper acts like the radius of a circle, we can use the length of the wiper blade as the radius. In this case, the length of the wiper blade is given as 75 cm. Therefore, the distance traveled by the tip of the windshield wiper is 75 cm * 2.2689 radians.
Calculating the distance:
distance = 75 cm * 2.2689 radians
distance = 170.17 cm (approximately)
Therefore, the tip of the windshield wiper travels approximately 170.17 cm in one swipe from left to right across the windshield.