Question

The vertical displacement, h(t),in metres, of a cork floating in rough water can be given by h(t)=0.5 cos(2t)+1, where t is the time , in seconds. Determine the maximum velocity that the cork achieves and the first time it occurs

Answer 1

Maximum=amplitude + resting position = 0.5 + 1 = 1.5

first time it occurs:
We can use the period because there's no phase shift
2pi/b
2pi/2
pi

So the first time it occurs is pi seconds.