The football team at Enormous State University (ESU) uses vector displacements to record its plays, with the origin taken to be the position of the ball before the play starts. In a certain pass play, the receiver starts at (1.0î − 5.0ĵ), where the units are yards, î is to the right, and ĵ is downfield. Subsequent displacements of the receiver are +9.0î (he is in motion before the snap), +11.0ĵ (breaks downfield), −6.0î + 4.0ĵ (zigs), and +12.0î + 18.0ĵ (zags). Meanwhile, the quarterback has dropped straight back to a position −7.0ĵ. How far and in which direction must the quarterback throw the ball? (Like the coach, you’ll be well advised to diagram the situation before solving this numerically.)
For this question, we are looking for the resultant vector. It is not really a “challenging problem”—that is, we simply need to convert English direction in relation to football to a coordinate system.
Start by writing the formula for the resultant vector using the four-step method.