Two dogs pull horizontally on ropes attached to a post; the angle between the ropes is 60.0°. If dog ?A? exerts a force of 270 N and dog ?B? exerts a force of 300 N. find the magnitude of the resultant force and the angle it makes with dog ?A?’s rope.

Solution 5E STEP 1: The force exerted by dog A is 270 N. The force exerted by dog B is 300 N. 0 The angle between the forces is 60 . The graphical representation is given below. By the law of parallelogram for vector addition, the vector R represents the resultant vector. This law follows the vector addition formula, 2 2 A + B = R = + B + 2AB cos ---------------------(1) 2 2 0 = 20 + 300 + 2 × 270 × 300 × cos 60 = 72900 + 90000 + 21000 = 183900 = 428.8 N . The magnitude of the resultant force is 428.8 N.