A wheel 5.00 ft in diameter rolls up a 15.0° incline. How far above the base of the incline is the top of

the wheel after the wheel has completed one revolution

same question from yesterday

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To find the height above the base of the incline that the top of the wheel is after one revolution, we can use trigonometry and the geometry of circles.

First, we need to determine the circumference of the wheel. The circumference (C) of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the diameter is given as 5.00 ft, so the radius is half of the diameter: r = 5.00 ft / 2 = 2.50 ft. Therefore, the circumference of the wheel is C = 2π(2.50 ft) = 5π ft.

Next, we need to find the distance the wheel travels vertically after one revolution. This can be calculated using the trigonometric relationship between angle, radius, and distance traveled on a circular path. The distance traveled vertically (h) is given by the formula h = C * sin(θ), where θ is the angle of incline.

In this case, the angle of the incline is given as 15.0°. So, the height above the base after one revolution is h = (5π ft) * sin(15.0°).

Now, let's calculate the value of sin(15.0°):

sin(15.0°) ≈ 0.25882

Therefore, the height above the base after one revolution is h ≈ (5π ft) * 0.25882 ≈ 4.084 ft.

Thus, the top of the wheel is approximately 4.084 ft above the base of the incline after completing one revolution.