Three forces with magnitudes of 74 pounds,98 pounds,and 105 pounds act on an object at angles 170°,220°,and 330°,respectively,with the positive x-axis.Find the magnitude and direction of the resultant force.Round answers to two decimal places.
A)99.08 pounds;240.95°
B)99.08 pounds;60.95°
C)117.42 pounds;240.95°
D)139.13 pounds;272.47°
E)117.42 pounds;60.95°

Question

Quizplus · Accepted Answer

Using vector addition, we get:

$R_x = 74\cos(170^\circ) + 98\cos(220^\circ) + 105\cos(330^\circ) \approx -83.42$
$R_y = 74\sin(170^\circ) + 98\sin(220^\circ) + 105\sin(330^\circ) \approx -50.12$

$R = \sqrt{R_x^2 + R_y^2} \approx 117.42$ pounds

$	heta = 	an^{-1}\left(\frac{R_y}{R_x}ight) \approx 240.95^\circ$

Therefore, the magnitude of the resultant force is approximately 117.42 pounds and its direction is approximately 240.95° with respect to the positive x-axis. The answer is choice C.

Three Forces with Magnitudes of 74 Pounds,98 Pounds,and 105 Pounds