A force vector F with arrow1 points due east and has a magnitude of 105 newtons.

Question

A force vector F with arrow1 points due east and has a magnitude of 105 newtons. A second force F with arrow2 is added to F with arrow1. The resultant of the two vectors has a magnitude of 895 newtons and points along the east/west line. Find the magnitude and direction of F with arrow2. (Enter your answers from smallest to largest.)

smallest magnitude ???N in what direction (due east/due west)

largest magnitude   ???N in what direction (due east/due west)

I'm just lost after 3 hours of looking at it and the book.

Explanation / Answer

Let east represent unit vector (+i) and west (- i), let north be + j

F1 = 105 i

let

F2 = a i + b j

----------------------------

Resultant is either R = 895 i (for east) or R = - 895 i (for west)

R= F1 + F2

1st case>

895 i = (105 i) + (a i + b j)

Comparing coefficients of i and j

a + 105 = 895 >>>>>>> gives a = 790

b = 0

F2 = 790 i + 0 = 790 i

|F2| = 790 N (ans)

Direction of F2 = east (ans)

--------------------------------------...

2nd case>

- 895 i = 105 i + a i + b j

comparing coefficients of i and j

a + 105 = - 895 >>>>>>> gives a = - 1000

b = 0

F2 = - 1000 i + 0 = - 1000 i = 1000 (- i)

|F2| = 1000 N (ans)

Direction of F2 = west (ans)

Hope this helps :)

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