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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.

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could u draw the game play lines? and maybe label them.. im not familiar with football
Haha me neither, it's just the wording of the problem
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?

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awesome thanks!

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