Okay, we are looking for two equations in the two unknowns v and . Let's first look at the range problem:
<-- y = 0 because the ball is back on the ground.
We need to solve the y equation for t:
<-- t = 0 is also a solution. I'm discarding it for obvious reasons.
And we plug that into the x equation:
This is our first equation.
Now let's look at the path of the ball intersecting the point (x, y) = (22.5 m, 11.25 m):
<-- This is not the same t as in the range equation!
This time I'm going to solve the x equation for t:
and insert it into the y equation:
This is our second equation.
So we have to solve the simultaneous equations:
There are a variety of ways to attack this system. After staring at it for a while I decided that this was probably the most direct way to do it. Solve the first equation for :
and insert this into the bottom equation:
At first glance this looks awful, but simplifying a bit:
which you can solve for without any further difficulties.
Let's see how you do from this point on.