SOLVED: A Ferris wheel has a radius of 10 m, and the bottom of the wheel passes 1 m above the ground. If the Ferris wheel makes one complete revolution every 20 s, find an equation that gives the height above the ground of a person on the Ferris wheel as (2024)
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Expert-Verified Answer. Final Answer: The height equation for a person on the Ferris wheel is h(t) = 10 * sin((π/10) * t) + 11. This equation considers the wheel's radius, ground clearance, and one revolution every 20 seconds.
Concept :- The distance covered by a wheel in one rotation is equal to its CIRCUMFERENCE! So here, if the radius (R) = 42cm, the circumference (C) => 2πR = 2 x (22/7) x 48 = 264 cm. The required distance (D) is 396 m = 396 x 100 cm [1m = 100cm]. = D/C = 396 x 100/264 = 150.
The angle of rotation is the amount of rotation and is the angular analog of distance. The angle of rotation Δ θ Δ θ is the arc length divided by the radius of curvature. 1 revolution = 2 π 2 π rad = 360°.
The total distance covered in one revolution will be equal to the perimeter of the wheel. Finally, to find the total number of revolutions, divide the total distance by distance covered in one revolution.
This is of the form h = a + b cos ct, where: a =40m. This is the height of the axle of the Ferris Wheel. b =-30m. The magnitude of this number is the radius of the wheel.
i Radius of wheel r = 42 cm Circumference i.e. distance travelled in 1 revolution = 2πr = 2 x 22/7 x 42 = 264 cm ii Distance travelled in 50 revolutions = 264 x 50 = 13200 cm = 132 m iii Distance travelled in 200 revolutions = 264 x 200 = 52800 cm = 528 m Hence i 264 cm ii 132 m iii 528 m.
When we figure out the circumference, we will know how far it will travel in one rotation. We will then need to multiply that value by 4 to see how far it will travel in 4 rotations. The wheels circumference is equivalent to 2*pi*radius. Or C=pi*diameter.
A wheel will travel its circumference once a revolution. Therefore, the distance traveled per revolution is pi*d. Of course, slippage, imperfections, etc. will make this slightly off.
For every 1 revolution, the wheel will travel a distance equal to its circumference. Q. Distance travelled by a circular wheel of diameter d cm in one revolution is 2πd.
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