How Should a Quarterback Throw to Hit a Stationary Receiver?

[Natko]

Homework Statement

A quarterback is running across the field, parallel to the line of scrimmage, at a constant speed of 2.5m/s, when he spots an open, stationary receiver straight downfield from him (ie, in a line parallel to the sidelines). If he can throw the football at a speed of 8.0m/s, relative to himself, at what angle, relative to the sidelines, must he throw it in order to hit the receiver? How far downfield was the receiver?

Homework Equations

Pythagorean theorem
SOH CAH TOA

The Attempt at a Solution

 

[haruspex]

Your diagram performs the vector sum of two velocities at right angles. You sum two velocity vectors if one of them represents a velocity relative to the other. But the relative velocity is not given here - it's the thing you are trying to find.
See if you can get the right diagram.

 

[Natko]

Does this look better?

Sorry, it's flipped on PF even though I rotated it on my computer.

 

[haruspex]

Does this look better?

Yes, except that the arrow on the 8m/s goes the wrong way. When adding vectors diagrammatically, the contributing vectors connect nose-to-tail; the resultant runs from the tail of the first to the nose of the last.