Mechanics projectiles AQA math A level

Q. Emma is in a park with her dog, Roxy. Emma throws a ball and Roxy catches it in
her mouth. The ground in the park is horizontal. Emma throws the ball from a point
at a height of 1.2 metres above the ground and Roxy catches the ball when it is at a
height of 0.5 metres above the ground. Emma throws the ball with an initial velocity of
8ms^-1 at an angle of 30 degrees above the horizontal.

(c) During the flight, the speed of the ball is a maximum when it is at a height of h metres
above the ground. Write down the value of h. (1)

(d) Find the maximum speed of the ball during its flight. (4)

I don't know how to solve this type of question. I have seen maximum height where v=0 question but none of maximum speed questions before. There's none on youtube either can anyone please help asap?

Using suvat, the speed in each direction is a constant or linear function of t. Just write down the equations.
So it should be fairly easy to work out where the max value will be.

For (c), I've done suvat
Vertical component, upward set as positive:
s: - 0.7
u: 8sin30
v: ?
a: - 9.8
t:

v^2 = u^2 + 2as
v^2 = 16 + 13.72 = 29.72
so, v = 5.45 ms^-1
5.45 is larger than u ms^-1 which is 8sin30 = 4ms^-1,
So max speed when h = 0.5 m. (This 'h=0.5 m' was the correct answer! 1 mark)

For (d),
Max speed so magnitude of velocity in horizontal And vertical component
So
Max speed = square root (5.45^2 + (8cos40)^2) = 8.82 ms-1 . This was the correct answe as well!
5.45 is the final velocity v for vertical component and
8cos40 is the initial velocity for horizontal component.

However, what I don't understand is that for calculating max speed, the FINAL velocity is used for vertical component but why ISN'T the final velocity of Horizontal component as well? Why is the INITIAL velocity of horizontal component used?

I tried calculating the final velocity of horizontal component but I couldn't because I didn't know the displacement for horizontal component, so i thought this might be the reason...
But still, I don't understand. Why is this?? Thank you!!