http://session.masteringphysics.com/problemAsset/1259764/2/YF-01-34.jpg (a) For

Question

http://session.masteringphysics.com/problemAsset/1259764/2/YF-01-34.jpg (a) For the vectors A and B in the figure (Figure 1) , use the method of components to find the magnitude of the vectors sum . (b)Find the direction of the vectors sum . (A+B) (c) Find the magnitude of the vector sum .(B+A) (d)Find the direction of the vector sum .(B+A) (e)Find the magnitude of the vector difference .(A-B) (f) Find the direction of the vector difference .(A-B) (g)Find the magnitude of the vector difference .(B-A)

Explanation / Answer

a) A(0,-8)

B(15sin(30),15cos(30))=B(7.5,12.99)

==>A+B=(0+7.5,-8+12.99)=(7.5,4.99)

magnitude (A+B)=(7.52+4.992)=9m

b) direction tan-1(4.99/7.5)=33.6degree wrt x axis counter clock wise

c)A+B=B+A hence

9m

d)33.6 degre w.r.t x axis in counter clockwise

e)A-B=(0-7.5,-8-4.99)=(-7.5.-12.99)

magnitude =(7.52+12.992)15.0m

f)direction tan-1(-12.99/-7.5)60 degree as both x and y component are negative hence

it makes 180-60=120 degree clockwise wrt x axis

g)magnitud of A-B = magnitude B-A

15m

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