The resultant of two forces acting on a body has a magnitude of 60 pounds. The angle between the 28-pound force and the resultant is 50°. Find the magnitude of the other force. a. 66.3 pounds b. 47.2 pounds c. 80.9 pounds d. 59.3 pounds 2. Without the wind, a plane would fly due east at a rate of 150 mph. The wind is blowing southeast at a rate of 50 mph. The wind is blowing at a 45° angle from due east. How far off of the due east path does the wind blow the plane? a. 5.3° b. 7.5° c. 10.8° d. 0.2°

1. We will use the Cosine Law:

x² = 60² + 28² - 2 · 60 · 28 · cos 50°

x² = 3,600 + 784 - 3360 · 0.6428

x² = 2,224.234

x = √2,224.234

x = 47.16 pounds ≈ 47.2

Answer: B) 47.2 pounds

2. By the Cosine Law (angle of 135° is opposite the forces resultant):

R² = 150² + 50² - 2 · 150 · 50 · cos 135°

R² = 22,500+2,500 - 15,000 · (-0.71)

R² = 35,650

R = √35,650 = 188.812 mph

After that we will use the Sine Law:

50 / sin α = 188.812 / sin 135°

50 / sin α = 188.812 / 0.71

sin α = 50 · 0.71 / 188.812

sin α = 0.188

α = sin^ (-1) 0.188

α = 10.83° ≈ 10.8°

Answer: C) 10.8°