Question

1. A boy noticed that the wind was blowing 30m/s 30degree with vertical.he ran with a speed of 40m/s 0 degree. Calculate the magnitude using the cosine law.

2.calculate the magnitude and direction if the vector A is 5N, 0 degree C is 7N, 110 degree,D is 2N, 22 degree E is 6N, 55degree with the horizontal. Calculate the magnitude and direction of a vector.

Answer 1

1 Apply the cosine law:

$$a=\sqrt{b^2+c^2-2bc\cos\theta},\\ a=\sqrt{30^2+40^2-2·30·40\cos30°}=20.5\text{ m/s}.$$

2 The components:

$$A_x=5\text{ N},\\ A_y=0.\\ C_x=7\cos110°=-2.4\text{ N},\\ C_y=7\sin110°=6.6\text{ N}.\\ D_x=2\cos22°=1.9\text{ N},\\ D_y=2\sin22°=0.75\text{ N}.\\ E_x=6\cos55°=3.4\text{ N},\\ E_y=6\sin55°=4.9\text{ N}.\\\space\\ R_x=A_x+C_x+D_x+E_x=7.9\text{ N},\\ R_y=A_y+C_y+D_y+E_y=12\text{ N}.\\ R=\sqrt{R_x^2+R_y^2}=14\text{ N}.$$