This is actually more a mathematics question than a physics question.

Thus I will assume that such real world issues as aerodynamic drag can be ignored.

So it starts off as a geometry problem,

how much of the speed is upwards and how much is horizontal?

Then how long will it take to reach the posts given the horizontal speed you have just calculated.

The next parts require you to include gravity

You should know the standard equation:

V=U+At

where:

U is the initial vertical component of the speed,

V is the current velocity (at time t)

A is the acceleration due to gravity.

Note that A is in the opposite direction to U

(i.e. if we say U is positive A must be negative).

You worked out earlier how long the ball takes to reach the posts

this is the time you need in the above equation.

For the last part you need the standard equation:

S=Ut+½At²

Where S is the distance traveled

since we have split the speed into vertical and horizontal components,

just consider the vertical component.

So if U is the initial vertical component of the speed and A is the acceleration (or if you prefer deceleration, because it is negative in this case) due to gravity

Then S is the height above the ground.

The question is now when is S zero?

There are two times when S is zero, one at the start (when it is first kicked) and one at the end (when it hits the ground).

Note that S=Ut+½At² is a quadratic equation.

There is a standard way of finding the roots of a quadratic equation (the points at which it is zero).

https://en.wikipedia.org/wiki/Quadratic_formula