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

Try graphing it

Answer 2

where the function reaches its maximum is where it is at and find the first time it happens

Answer 3

thnks

Answer 4

Yes what @darkknight said or you could determine the maximum by applying the first/second derivative test or know the formula for extrema of a sinusoidal function:

For any sinusoidal function in the form of
\(Asin(Bx+C)+D\)
or
\(Acos(Bx+C)+D\)
the local maxima can be determined by the formula \(D+|A|\) and the local minima can be determined by the formula \(D-|A|\).

Answer 5

\(\color{#0cbb34}{\text{Originally Posted by}}\) @roughpiglet
thnks
\(\color{#0cbb34}{\text{End of Quote}}\)
yw