Answer: 86.6ft closer to the ground.
Step-by-step explanation:
The diameter of the wheel is 200ft
Then the radius, half of the diameter, is: r = 200ft/2 = 100ft.
Initially, the seat is at the same level that the center of the wheel.
And the distance between the center of the wheel and the bottom is the radius.
Then the initial position is at an angle of 0° from the x-axis. (where the (0,0) of this axis coincides with the center of the wheel=
Now, the wheel rotates 60°. (downwards, so we actually could use -60° measuring from the positive x-axis)
And thinking in this as a triangle rectangle, where the opposite angle is 60°, we can calculate the displacement in the vertical direction as:
y = sin(-60°)*R
y = sin(-60°)*100ft = -86.6ft
So the seat is 86.6ft closer to the ground.
