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.

Question

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.

Answer 1

So clearly the amplitude is .9 m
2π/k = period
2π/k = 4
4k = 2π
k = π/2

but we want the low point to be 0 not -.9
so height = .9sin(π/2 t), where t is in seconds and height is in metres

Answer 2

oops, pressed "submit" too soon , forgot to raise that boat:

height = .9sin(π/2 t) + .9

b) .9sin(π/2 t) + .9 > ?? ( is the normal position the water level, that is , zero
or is it 0.9 ? You decide, you will get 2 answers.)

Answer 3

y=0.9sin(pie/2t)

Answer 4

Reiny, you are not right. The textbook answers say otherwise. 😡😡😡