Question

Two forces of 3N and 2N are acting at an angle of 45 to each other. Find the magnitude and direction of the resultant force?

Answer 1

3 in x direction

2 /sqrt 2 in x and 2/sqrt2 in y

x force = 3 + 2/sqrt2
y force = 2/sqrt 2

}F} = sqrt [ (3 + 2/sqrt2)^2 + 9 ]

tan angle above x axis = [ (2/sqt2)/(3 +2/sqrt2)]

Answer 2

or

complete the parallelogram
r^2 = 3^2 + 2^2 - 2(3)(2)cos135°
= 13 - 12(-1/√2)
r = appr 4.6 N

or

direction vector = (3,0) + (2cos45, 2sin45)
= (3,0) + (1.414, 1.414) = (4.414 , 1.414)
magnitude = √(4.414^2 + 1.414^2) = appr 4.6