resultant displacement

Question

A quarterback takes the ball from the line of scrimmage, runs backward for 11.0 yards, then runs sideways parallel to the line of scrimmage for 12.0 yards. At this point, he throws a 30.0 yard forward pass straight down the ?eld. What is the magnitude of the football’s resultant displacement?

Answer 1

The football will end up at a point 19 yards ahead of the line of scrimmage and 12 yards to the side.  So the magnitude of the displacement will be sqrt (19² + 12²) = sqrt (505) = 22.5 yards

 

 

 

Answer 2

Using vectors:

 

< 0, -10>        backward run

<12, 0>          sideways pass

<0, 30>          forward pitch

 

Add these together

 

<12, 20>        the magnitude is the square root of the sum of squares of the two components, i.e. Pythagoras

 

144 + 400 = d²

544 = d²

23.32≈ d

 

The displacement is approximately 23.32 feet.