Three people (you and two friends) are pulling a sled across ice. YOU are person

Question

Three people (you and two friends) are pulling a sled across ice. YOU are person #3. The figure is a view from ABOVE, looking down on the sled and the three People. The forces of person 1 and person two are known: F1 = 12i + 9j F2 = 18i + 7j (a) You apply Force 3. As a result, the total force (the sum of the three forces) is to the right, so in the positive i direction. The MAGNITUDE of the total force is 44 (units are Newtons). Obtain F3 in vector notation: What angle does Force 3 make with respect to the positive i direction?

Explanation / Answer

I have taken x and y instead of i cap and j cap respectively

A)

Let the force F3 be a x + b y

F1 = 12x + 9y

F2 = 18x + 7y

Total force = F1 + F2 +F3 = 44 x + 0y

(12x + 9y) + (18x + 7y) + ( a x + b y ) = 44x + 0y

(12+18+a)x + (9+7+b)y = 44x + 0y

Comparing both sides, we have

a=14 and b= -16

Thus, F3 = 14x - 16y

B)

Now, let F3 make angle theta with positive x axis,

then, theta = tan-1(16/14) = 48.81

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