Question

Two people swing a jump rope. The highest point in the middle of the jump rope is 76 inches above the ground, and the lowest point is 4 inches. The rope makes 4 revolutions per second. Write a model for the height of the rope in inches as a function of time in seconds given that the rope starts at its lowest point.

Answer 1

See image below

Explanation:

Answer 2

h(t) = 36sin(1440x)+ 40

Explanation:

Given the information:

• highest point: 76 inches=>
• lowest point: 4 inches =>
• 4 revolutions per second => period:
  `(1)/(4)` per second =
  `(360)/((1)/(4) ) =1440`

y = a sin (bx+c) + k for different values of a, b, and c

=> Amplitude (a) = (highest point - lowest point) / 2 = 36

=> asymptom (k) = (highest point - lowest point) / 2 = 40

=> model for the height of the rope in inches as a function of time in seconds given that the rope starts at its lowest point is:

h(t) = 36sin(1440x)+ 40

Hope it will find you well.