How Do You Calculate the Resultant Displacement in a Football Pass Scenario?

[joedango]

In a game of American football, a quarterback takes the ball from the line of scrimmage, runs backward for 10.5 yards, and then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a forward pass 55.0 yards straight downfield perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?

From my drawing I get a right triangle with one side being 15 yd and the other side being 55 yds. In my attempt I do magnitude = , but 57.01 is not the right answer. What am I doing wrong?

 

[Spinnor]

You are forgetting the part where he runs back 10 yards.

 

[Spinnor]

See maybe:

http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

 

[joedango]

Oh I got it thanks!

 

[rwisz]

I would approach this problem by breaking it down into smaller components and using vector addition to find the resultant displacement. First, I would draw a diagram of the situation to visualize the motion of the quarterback and the football.

Next, I would use the Pythagorean theorem to find the magnitude of the displacement caused by the quarterback running backwards and sideways. The resultant displacement would be the hypotenuse of the right triangle formed by the two sides, with a magnitude of approximately 18.4 yards.

To find the magnitude of the football's displacement, I would use the Pythagorean theorem again, this time with the 55-yard forward pass and the 18.4-yard displacement as the two sides of the right triangle. The resultant displacement of the football would have a magnitude of approximately 57.1 yards.

It is important to note that the magnitude of the resultant displacement may not necessarily be equal to the distance traveled by the football, as it is affected by both the horizontal and vertical components of its motion. This is why simply adding the distances traveled by the quarterback and the football does not give the correct answer.

In conclusion, to find the magnitude of the football's resultant displacement, we must consider both the horizontal and vertical components of its motion and use vector addition to find the resultant displacement.