Who gave you this problem, anyway, and what are they trying to prove by giving it to you??

Okay, we are looking for two equations in the two unknowns v and . Let's first look at the range problem:

and

<-- 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 isnotthe same t as in the range equation!

and

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.

-Dan