A wave travels along a string, and its position in millimeters is described by $h\left(t\right)=15(2\cos t+1)$, for $t\ge 0$, where $t$ represents time in seconds. Determine the times and positions at which the velocity is zero.

The velocity is zero for $t=n\pi$, where $n$ is any nonnegative integer.

The position is $60\text{ mm}$ if $n$ is even or $-20\text{ mm}$ if $n$ is odd.

The velocity is zero for $t=n\pi$, where $n$ is any nonnegative integer.

The position is $45\text{ mm}$ if $n$ is even or $-15\text{ mm}$ if $n$ is odd.

The velocity is zero for $t=2n\pi$, where $n$ is any nonnegative integer.

The position is $60\text{ mm}$ if $n$ is even or $-20\text{ mm}$ if $n$ is odd.

The velocity is zero for $t=2n\pi$, where $n$ is any nonnegative integer.

The position is $45\text{ mm}$ if $n$ is even or $-15\text{ mm}$ if $n$ is odd.