How Can I Find the Initial Velocity of a Ball Based on Angle and Window Height?

[Kernul]

Homework Statement

A boy kicks a ball with an initial velocity v₀ that forms an angle of 30° with the x. The ball, at the culmination of the trajectory, enters a window at a height of 9.8 m. Find the module of the initial velocity and the time used by the ball to reach the window. Also find the range from the initial position of the ball to the window.

Homework Equations

How do I find the initial velocity knowing just the angle and the height of the window?

The Attempt at a Solution

I tried with this equations but I still don't know how to proceed:
x = v₀ * cos 30° * t
y = v₀ * sin 30° * t - 1/2 * g * t²
because even if I try something like this:
t = x / v₀ * cos 30°
and then I change with this in the second equation there is still the fact that I do not know the value of x.

 

[LittleMrsMonkey]

I believe by "culmination of the trajectory" it means that 9.8 m is the maximum height it can reach,which makes the problem quite easy if that's the case.

 

[Kernul]

Oh! So I have to think of it as the maximum height!
Okay, thank you!

 

[LittleMrsMonkey]

I don't have any more reason to think so than you do,though.