Question

The vertical component of the projectile motion of an object depends on which of these? initial velocity or angel of trajectory

Answer 1

It depends on both of them.

In fact, the projectile begins its motion with an initial velocity of $v_0$ and an angle of $\alpha$. On the y-axis (vertical direction), it is an accelerated motion with acceleration equal to -g (gravitational acceleration). The vertical velocity of the projectile at any time t is given by
$v_y (t) = v_0 sin \alpha + gt$
and as it can be seen, this depends on both initial velocity and angle.