Question

Tarzan is swinging back and forth on his grapevine. As he swings, he goes back and forth across the riverbank, going alternately over land and water. Jane decides to model his motion mathematically and starts her stopwatch. Let t be the number of seconds the stopwatch reads and let y be the number of meters Tarzan is from the riverbank. Assume that y varies sinusoidally with t, and that y is positive when Tarzan is over water and negative when he is over land. Jane finds that when t = 2, Tarzan is at one end of his swing, where y = -25. She finds that when t = 7, Tarzan reaches the other end of his swing where y = 19. Sketch a graph of this function in terms of time, t, beginning from the phase shift. Then find the equation of the function.

Answer 1

The sinusoidal wave is .

When The minimum point is

When The maximum point is

The midpoint intercepts are

Amplitude

Tarzan takes seconds to go from one end to another end. i.e., he takes 10 seconds to complete one cycle. So the angular frequency is .

The function is maximum at , so the phase lag is

Hence the sinusoidal wave function is