Question

Two people swing jump ropes, as shown in the diagram. The highest point of the middle of each rope is 73 inches above the ground, and the lowest point is 5 inches. The rope makes 1 revolution per second. Write a model for the height h (in inches) of a rope as a function of the time t (in seconds) given that the rope is at its lowest point when t=0.

a) h(t)=39sin(2πt)+39
b) h(t)=39cos(2πt)+39
c) h(t)=34sin(2πt)+34
d) h(t)=34cos(2πt)+34

Answer 1

The model for the height of a rope as a function of time is h(t) = 39sin(2πt) + 39.

Step-by-step explanation:

The model for the height h (in inches) of a rope as a function of time t (in seconds) is given by option a) h(t) = 39sin(2πt) + 39.

This equation represents a sinusoidal function, where the amplitude of the wave is 39 inches and the period of the wave is 1 second. The sine function oscillates between -1 and 1, so adding 39 to the function raises the lowest point of the rope to 39 inches above the ground.