A boat tied up at a dock bobs up & down with the passing waves. Vertical distance between its high & low points is 1.8 m.The cycle is repeated...

The boat moves up and down with the passing waves. I take
the height of the boat to be a sinusoidal function. And the height of the boat is zero
at the start of the cycle.

The distance between the high
and the low points is 1.8. So the amplitude of the vertical displacement is 1.8/2 = 0.9
m.

As the cycle is repeated every 4 s, the time period is
4s.

The equation of the motion of the boat as it bobs up
and down is given by f(t) = 0.9*sin ((t - 4)*0.5*pi)

The
rate of change of the vertical velocity is the derivative of f(t), f'(t) =
0.9*0.5*pi*cos ((t - 4)*0.5*pi).

The instantaneous rate of
change of velocity is 0 when 0.9*0.5*pi*cos ((t - 4)*0.5*pi) =
0

or at t = 1 + n*4 and at t = 3 +
n*4

The instantaneous rate of change is maximum at t = 0 +
4*n and at t= 2 + n*4

Therefore the instantaneous rate of
change in the vertical position is :

0 at t =
1 + n*4 and t = 3 + n*4 and maximum at t = 0 + 4*n and t= 2 +
n*4