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QUESTION: In a football game, a quarterback (G), hit simultaneously by two linebackers, experiences horizontal forces of 412 N [27.0 W of N] and 478 N [36.0 N of E]. Determine the net force of the quarterback.

ANSWER: Hello James,

Convert both forces into their components in the North and East directions.
F1n = 412*cos27
To find F1e, first figure what F1w would be
F1w = 412*sin27
F1e = -F1w = -412*sin27

F2n = 478*sin36
F2e = 478*cos36

Then sum the components pointing North (call the result Fn) and the components pointing E (call the result Fe). Then use Pythagoras to find the resultant of those Northward and Eastward components. Then the direction (N of E) is

I hope this helps,

---------- FOLLOW-UP ----------

QUESTION: Hi thank you so much for your help I really appreciate :D, but I was just wondering, for the second force why you used cos instead of sin for the eastward direction, like I know the way you showed me works but I'm confused.

Hi again James,

Well, I could have said F2e = 478*sin54 but it seems like that would add confusion.

The 478 is the hypotenuse of the rectangle you get when you draw the original vector and its North and East components. And F2e is the side adjacent to the 36 degree angle. So
cos36 = side adjacent/hypotenuse = F2e/278
and therefore F2e = 278*cos36.

I hope this helps,


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Steve Johnson


I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.


I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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