## catsrule332 Group Title Two people pull on a stubborn mule. One person pulls at a 70 degree angle with 50 lbs of force, and the other person pulls at a 100 degree angle with 40 lbs of force. Find the single force that is equivalent to the two forces. Find a third force that a person would need to exert to make the resultant force equal to zero. Explain. 2 years ago 2 years ago

First, we need to take the dot product of the two vectors. $F_1 \cdot F_2 = |F_1||F_2| \cos(\theta_2 - \theta_1)$ Second, we need to find the components of each force and add them. $F_x = F_1 \cos(\theta_1) + F_2 \cos(\theta_2)$$F_y = F_1 \sin(\theta_1) + F_2 \sin(\theta_2)$The third force must be equal but opposite to these. The angle at which this force acts$\tan^{-1} \left( \left \vert F_y \over F_x \right \vert \right )$