Milton is floating in an inner tube in a wave pool. He is 1.5 m from the bottom of the pool when he is at the trough of a wave. A stopwatch starts timing at this point. In 1.25 s, he is on the crest of the wave, 2.1 m from the bottom of the pool. a) Determine the equation of the function that expresses Milton's distance from the bottom of the pool in terms of time.
This is the concept of sinusoidal, to solve the question we proceed as follows; Using the formula; g(t)=offset+A*sin[(2πt)/T+Delay] From sinusoidal theory, the time from trough to crest is normally half the period of the wave form. Such that T=2.5 The pick magnitude is given by: Trough-Crest= 2.1-1.5=0.6 m amplitude=1/2(Trough-Crest) =1/2*0.6 =0.3 The offset to the center of the circle is 0.3+1.5=1.8 Since the delay is at -π/2 the wave will start at the trough at [time,t=0] substituting the above in our formula we get: g(t)=1.8+(0.3)sin[(2*π*t)/2.5]-π/2] g(t)=1.8+0.3sin[(0.8πt)/T-π/2]
