Question #149697
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°
1
Expert's answer
2020-12-10T11:07:12-0500

a) The components are:


vx=9.0mcos60°=4.5mvy=9.0msin60°=7.8mv_x = 9.0m\cdot \cos 60\degree =4.5 m\\ v_y = 9.0m\cdot \sin 60\degree =7.8m

b)The components are:


vx=15kmcos315°=10.6kmvy=15kmsin315°=10.6kmv_x = 15km\cdot \cos 315\degree =10.6 km\\ v_y = 15km\cdot \sin 315\degree =-10.6km

c)The components are:


vx=4.6cmcos14°=4.5cmvy=15kmsin315°=1.1cmv_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


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