Question

I am having trouble figuring out this question

Jan observes a buoy bobbing up and down through a total amplitude of 8 feet. Beginning at the top of the wave, if the buoy completes a full cycle every 8 seconds, what is the height of the buoy relative to its lowest point after 12 seconds?

I tried making a function out of what was given to me but I am missing so much information I don't understand dhow it would work.

Answer 1

amplitude=1/2 full swing=4feet
period = 8 seconds, or freq=1/8 second, or w=2PI/8 or PI/4 rad/sec

h=4cos(wt)=4cos(PI/4 * 12)=4cos 3PI

check that.

another way: the time is 1.5 periods, which means it has to be on the lowest point.

sketch the graph

Answer 2

where did the 12 come from?

Answer 3

oops sorry never mind

Answer 4

How do you know to use cos and not sine?

Answer 5

cos has value of 1 at t = 0 so that would be at the top of the wave as the problem stated.
Sin of 0 is 0 so that is not what you want.
You could do the same thing with a phase shift of pi/2 because
sin (90 deg -a) = cos a
sin (pi/2 - pi t/4) = cos (pi t/4)

Answer 6

oh I see thank you very much I totally get it now

Answer 7

By the way remember it is relative to the lowest point, not zero, so it is -4 + whatever your answer is.