This is, as you suggest, a "vector" problem. The problem, in the first problem, is to show that the ball will go "through the goal posts". If you set "x= 0" at the point where the kick starts, at the 30 yard line the goal post is at x= [and here, we have an problem. Is this "amateur football" or "professional football"? "Amateur football" (highschool, college) has the goal posts on the goal line, x= 30. But "professional football" has it 10 yards behind the goal line, x= 40]. Again, taking "z= 0" at the point where the kick starts, we need to have z, at the point the ball passes the goal post to be at least the height of the goal post. That is the same for both amateur and professional football but what is it? You will also need to find the width of the goal posts.
Now, with all that, assume that the ball is kicked at an angle of [itex]\theta[/itex] degrees to the horizontal, as well as your given 79 degrees to the yard line. You can then calculate that the initial velocity vector is . Of course, the basic rule here is that the constant acceleration is that due to gravity [tex]\left<0, 0, -g\right>[tex] with g= -9.87 m/s^2. After t seconds, the velocity vector will be where that last vector is the wind velocity. Then, of course, you can find the position vector at each second, t, by integrating. However, I notice that this is posted under "preCalculus" and I don't know any way to do this without Calculus- unless you are given a formula for motion under at constant acceleration.