The time taken to reach maximum height in projectile motion is determined by the vertical component of the initial velocity, which is given by $u\sin\theta$. At maximum height, the vertical velocity becomes zero, and using the equation of motion $v = u + at$, where $v = 0$ and $a = -g$, leads to the expression $t = \frac{u\sin\theta}{g}$. This formula reflects the relationship between the initial vertical velocity, gravitational acceleration, and time.