# Quarterback?

A quarterback takes the ball from the line of scrimmage, runs backward for 11.3 yd, then runs sideways parallel to the line of scrimmage for 17.1 yd. At this point, he throws a 48.7 yd forward pass straight downfield, perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?

Relevance

The resultant displacement can be found using a right triangle and Pythagorean theorem. Drawing a diagram also helps, so try that.

First, you have to find the legs of this triangle. The leg parallel to the line of scrimmage is 17.1 yds. The leg perpendicular to the line of scrimmage is defined by 48.7-11.3 = 37.4 yds. Since you are finding the displacement from the original position of the quarterback, you have to take into account the distance be went backward.

Now that you have both legs, you can find the hypotenuse, which is the resultant displacement. Using the Pythagorean theorem (a^2+b^2=c^2), solve for c.

Thus, resultant displacement is sqrt(17.1^2 + 37.4^2) = 41.12 yds

Hope this helps

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