Daniell Phillips

2021-12-17

A quarterback takes the ball from the line of scrimmage, runs backwards for 10.0 yards, then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a 50.0-yard forward pass straight downfield, perpendicular to the line of scrimmage. What is the magnitude of the football’s resultant displacement?

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eninsala06

Expert

Let us denote the displacements of the ball made by the quarterback as: $\mathrm{△}\stackrel{\to }{{R}_{1}},\mathrm{△}\stackrel{\to }{{R}_{2}}$ and $\stackrel{\to }{{R}_{3}}$. These are: running backwards for 10 yards, running parallel to the line of scrimmage, sideways, for 15 yards and throwing the ball 50 yards forward respectively.
We can calculate the resulting displacement, $\mathrm{△}\stackrel{\to }{R}$ by adding all of the displacements. The order in which we do it shouldnt

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