A buoy is floating in the sea, bobbing up and down with the waves. The height H H (in feet) of the buoy above the sea level after t t seconds is given by the function H ( t ) = 3 cos ⁡ t − 3 sin ⁡ t H\left(t\right)=3\cos t-3\sin t , for t ≥ 0 t\geq{0} . Determine the times at which the velocity of the buoy is zero.

t = n π − π 4 seconds t=n\pi-\frac{\pi}{4}~\text{seconds} t = nπ − 4 π seconds , where n n n is any positive integer

t = 1 4 n π seconds t=\frac14n\pi~\text{seconds} , where n n is any nonnegative integer

t = 1 2 n π seconds t=\frac12n\pi~\text{seconds} , where n n n is any nonnegative integer

t = n π + π 4 seconds t=n\pi+\frac{\pi}{4}~\text{seconds} , where n n n is any positive integer

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4. Applications of Derivatives

Motion Analysis

4. Applications of Derivatives

Motion Analysis: Study with Video Lessons, Practice Problems & Examples

22PRACTICE PROBLEM

ANSWERS OPTIONS

$t = \frac{1}{4} n π seconds$ , where $n$ is any nonnegative integer

$t = \frac{1}{2} n π seconds$ , where $n$ is any nonnegative integer

$t = n π + \frac{π}{4} seconds$ , where $n$ is any positive integer

$t=n\pi-\frac{\pi}{4}~\text{seconds}$ , where $n$ is any positive integer