Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° and 160° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

u = 100 (cos 50), (sin 50) = (64.28),(76.60)
v = 50 (cos 160), (sin 160) = (-46.98),(17.10)

w = u + v
w = (64.28 + -46.98), (76.60 + 17.10)
w = (15.30),(93.70)

||w|| = √((15.3)^2+(93.7)^2)
||w|| = 94.94 = magnitude

Now how do I find direction from here?

Question

Two forces with magnitudes of 100 and 50 pounds act on an object at angles of 50° and 160° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.

u = 100 (cos 50), (sin 50) = (64.28),(76.60)
v = 50 (cos 160), (sin 160) = (-46.98),(17.10)

w = u + v
w = (64.28 + -46.98), (76.60 + 17.10)
w = (15.30),(93.70)

||w|| = √((15.3)^2+(93.7)^2)
||w|| = 94.94 = magnitude

Now how do I find direction from here?

anonymous · Answer

I was taught that it's tan^-1 (93.7/15.3) but I get about 80 degrees which makes no sense seeing that the two forces are coming from the first and second quadrant, shouldn't the direction be going into the third or fourth?

loser66 · Answer

w = (15.30, 93.70) 
magnitude is 94.94 therefore, polar form of w is w= 94.94 ( 15.30/94.94, 93.70/94.94) 
calculate it, and let the first term (inside of the parenthesis) = cos (theta), the second term = sin (theta). then, solve for theta, you have the direction of w

loser66 · Answer

hey, 80 degree is in the first quadrant, your tan is positive which means both cos and sin in the first or the third quadrant.

loser66 · Answer

it makes perfect sense, friend

anonymous · Answer

So it can be in the third quadrant?

loser66 · Answer

your way is get tan from the formula and there is no way to figure out the right answer without calculator. I am not allowed to use calculator. So, I have to calculate the angle by my way to consider which quadrant my angle is. Your result is 80 degree. no need to consider the third quadrant because 80 degree cannot be in the third quadrant, right?

anonymous · Answer

But tangent can be positive in both the 1st and third quadrant: What discerns from which way it is?|dw:1375558311663:dw|

loser66 · Answer

nope

anonymous · Answer

So the terminal direction faces upward?

loser66 · Answer

yours is perfect, don't confuse yourself by anything else.

aivantettet26 · Answer

$$\theta = \tan^-1(\frac yx)$$

aivantettet26 · Answer

theta = tan^-1 (93.71/17.3)
is equals to
theta = 79.54 deg North of East
since Sigma X and Sigma Y are all positive therefore the resultant force is in the first quadrant.

aivantettet26 · Answer

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aivantettet26 · Answer

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