s=seconds; rad=radians; pi=3.14...; ft=feet; t=time n=any non-negative integer
A merry-go-round rotates at a constant angular velocity of 2pi/5 rad/s, while rings of seats rotate at a different (but constant) angular velocity of pi rad/s. Both the seats and Merry-go-round are rotating counter-clockwise at a rate of 4pi ft/s. The radius of the circle of seats is 4 ft, and the radius of the merry-go-round is 10 ft. the closest point of the seats to the center of the merry-go-round is 2 ft from it. there is a fence, where, when t=0 s, your seat is furthest from the fence: 23 feet away (the fence is 3 feet from the edge of the merry-go-round).
I need to find the equation of the distance of the seat from the fence.
I calculated that the seat (alone) makes 1 rev/2 s, and the merry-go-round makes 1 rev/5 s. One period is 10 s (least common multiple). the equations for the merry-go-round (in relation to the fence) and the seats (in relation to the center of the merry-go-round) are, respectively, y=10cos((2pi/5)x)+13 and y=4cos(pi*x)+6
A merry-go-round rotates at a constant angular velocity of 2pi/5 rad/s, while rings of seats rotate at a different (but constant) angular velocity of pi rad/s. Both the seats and Merry-go-round are rotating counter-clockwise at a rate of 4pi ft/s. The radius of the circle of seats is 4 ft, and the radius of the merry-go-round is 10 ft. the closest point of the seats to the center of the merry-go-round is 2 ft from it. there is a fence, where, when t=0 s, your seat is furthest from the fence: 23 feet away (the fence is 3 feet from the edge of the merry-go-round).
I need to find the equation of the distance of the seat from the fence.
I calculated that the seat (alone) makes 1 rev/2 s, and the merry-go-round makes 1 rev/5 s. One period is 10 s (least common multiple). the equations for the merry-go-round (in relation to the fence) and the seats (in relation to the center of the merry-go-round) are, respectively, y=10cos((2pi/5)x)+13 and y=4cos(pi*x)+6