A ferris wheel has a diameter of 50 meters. If point A is at the lowest point of the ferris wheel, 0 meters. What is the height of point A if the wheel moves 2pi/3 radians clockwise? What is the equation?
since cos(x) has it max at x=0, and you have a min there,
A(x) = 50(1-cos(x))
now just plug in x = 2pi/3
To find the height of point A when the ferris wheel moves 2π/3 radians clockwise, we can use the equation for the height of a point on a circle:
h = r - r * cos(θ)
where:
h = height of the point
r = radius of the ferris wheel
θ = angle in radians
Given that the diameter of the ferris wheel is 50 meters, we can find the radius by dividing the diameter by 2:
r = 50/2 = 25 meters
Since point A is at the lowest point, its initial height is 0 meters. Now we can substitute the values into the equation and solve for the height:
θ = 2π/3 radians
r = 25 meters
h = 25 - 25 * cos(2π/3)
We can then simplify and evaluate:
h = 25 - 25 * cos(120°)
Using a calculator or trigonometric table, we can find that cos(120°) ≈ -0.5. Therefore:
h = 25 - 25 * (-0.5)
h = 25 - (-12.5)
h = 25 + 12.5
h = 37.5 meters
So, the height of point A when the ferris wheel moves 2π/3 radians clockwise is 37.5 meters.