Here's the basic plan of attack for this kind of problem.
Always start by setting up and origin and coordinate system. I would put the origin where the ball was thrown with a +x axis in the direction of the horizontal component of the throw and a +y axis directly upward.
I will assume the ball is caught at the same height it was thrown at, since we have been given no information to the contrary.
Now list all of your information:
The ball is caught at time t at and .
Now, in this time, the receiver runs from the origin to x = 18 m in this same time t at a constant speed. So
So we need an expression for t.
Look back at the football data. We have essentially 5 equations at our disposal:
<-- Since this equation contains all the Physics.
From the x equation we get
Or we could use the first y equation:
My difficulty with this problem is that the two equations do not agree with what the time is. The only way I can correct for this is to assume that either the receiver is not at the level of the origin, or the quarterback isn't. If this is the case then we must choose the x equation to give us the time since this equation is not altered by a height change. I do not like the necessity of making this kind of logic chain, and I certainly would not expect a typical student to come up with it. It is standard in "throwing" problems like these to make the assumption that the projectile starts and ends at the same height unless otherwise explicitly stated in the problem.
So anyway I get that
Thus the receiver needs to run at
The other problems can be done using a similar setup.