Question

In a game of football, the quarterback takes the ball from the line of scrimmage, runs backward 10 yards, then sideways (parallel to line of scrimmage) 15 yards. He then throws a forward pass 50 yards downfield perpendicular to the line of scrimmage. What is the magnitude of the footballs displacement? Explain.

Answer 1

could u draw the game play lines? and maybe label them.. im not familiar with football

Answer 2

Haha me neither, it's just the wording of the problem

Answer 3

okay, so vector addition here, let's imagine that the ball starts at the origin (0,0). We'll let the y direction be downfield and the x direction be across field. The ball is first moved back 10 yards, so that's -10 in the y direction, or the vector (0,-10), then sideways 15 yards, or vector (15,0) and then forward 50 yards (0,50). in order to find the displacement vector we have to add up the components of these 3 vectors:
\[(0,-10)+(15,0)+(0,50) = (15,40)\]
now the magnitude of this displacement vector is the square root of the components squared:
\[D = \sqrt{x^2+y^2} = \sqrt{15^2+40^2}\]
I'm not going to do the math for you there, but you get the idea?

Answer 4

awesome thanks!