Moderate# Finding Maximum Velocity from a Vector Equation

APCALC-KEEMSF

The velocity of a particle for $t\geq0$ is given by the vector equation $\vec{v}=\left(2+2\sin{2t}\right)\vec{i}+\left(2+2\cos{2t}\right)\vec{j}$.

For the interval $\left[0, \cfrac{\pi}{2}\right]$ what is the maximum velocity of the particle in the vertical direction?