three dogs are fighting over a bone one pulls 50N N.E,and 60N N.W and the other 100N South.?

Question

calculate the resultant force of the bone

Answer 1

Break each force down into x and y components.

Let North be y-positive and east be x-positive

x-components: 50cos45 - 60 cos45 = 35.36 - 42.43 = -7.07 (ie west)

y -components: 50 Sin45 + 60 Sin45 - 100 = -22.21 (ie south)

Net force is SQRT ((7.07)^2 + (-22.21)^2) = 23.3 N

Direction: theta = arctan(22.21/7.07) = 72 degrees south of west

Answer 2

y:
-100 + 60 sin45 + 50 sin45 = -22.2 N
x:
50 cos45 - 60 cos45 = -7.07 N