Determine a sinusoidal equation.

A boat tied up at a dock bobs up and down with passing waves. The vertical distance between its high point and its low point is 1.8m and the cycle is repeated every 4 seconds.

a) Determine a sinusoidal equation to model the vertical position, in metres, of the boat versus the time, in seconds.

b) Use your model to determine when, during each cycle, the boat is 0.5m above its mean position. Round your answers to the nearest hundredth of a second.

I have a few questions..:

The answer for a) is y=0.9sin(pi/2t) why does that equation not show metres.. if I were to have my answer as 0.9msin(pi/2t) is that wrong? Also why is it sin? Why can't it be cos or tan? For question b can someone give me a hint as to what to do (Thinking)

it doesn't have metres in it purley because u assume that y is in metres therefore you just put that in at the end. How you have written it would be percieved as there being another variable m.

As for part b) you need to make y = 0.5 as its mean position will be y = 0. Making y = 0.5 this will give you times for t after solving. You should be able to work out what to do with them ....

I'm kind of confused. This is what I tried for b:

0.5 = 0.9sin(pi/2 t)

0.5 / (pi/2) = 0.9sin(t)

0.3184713376 = 0.7833269096 t

t = 0.4065624884

The 2 answers in the book are: t=0.37s, t=1.63s

How can there be 2 answers? What am I doing wrong?

Hmm now im really confused, how is it possible to have 2 answers for b? >.<

t=0.37s, t=1.63s

Within each complete cycle, it hits it once on the way up, and once on the way down.

First thing you need to do is imagine (or draw) a sine wave. Then looking at this wave you will see if you put a horizontal line anywhere it will cross twice per cycle.

So thinking of the boat bobbing in the waves it wil float up to 0.5m past up to 1.8m then on its way back down past 0.5m and down to -1.8m therfore there is two times.