Question

Use a scale drawing and find the x and y components of the following
vectors.In each case the magnitude of the vector and the angle measured
counterclockwise from the +x-axis.

a. Magnitude = 9.0 m , angle = 60°
b. Magnitude = 15.0 km, angle = 315°
c. Magnitude = 4.6 cm, angle = 14°

Answer 1

a) The components are:

$$v_x = 9.0m\cdot \cos 60\degree =4.5 m\\ v_y = 9.0m\cdot \sin 60\degree =7.8m$$

b)The components are:

$$v_x = 15km\cdot \cos 315\degree =10.6 km\\ v_y = 15km\cdot \sin 315\degree =-10.6km$$

c)The components are:

$$v_x = 4.6cm\cdot \cos 14\degree =4.5cm\\ v_y = 15km\cdot \sin 315\degree =1.1cm$$

The drawings are shown in the figure below