Question

Tim is floating in an inner tube in a wave pool. He is 1.5m from the bottom of the pool when he is at the trough(bottom) of the wave. A stopwatch starts timing at this point. In 1.25s, he is on the crest(top) of the wave, 2.1m from the bottom of the pool.

a) Write a sinusoidal function that represents the distance from the bottom of the pool in terms of time. The function must illustrate starting at the bottom of the pool. (4 marks)


b) How far above the bottom of the pool is time at t=4s? (2 marks)


c) If the period changes to 3s, what is the equation of the new function?

Answer 1

Answer: d(t)=0.3 ⋅ sin(2π/3⋅(t−0))+1.8