Question

1. A vector B = B_xi + B_yj, when added to the vector C = 3.0i + 4.0j, yields a resultant vector A that is in the negative y- direction and has a magnitude which is twice that of C. Find

(a) B_x and B_y,

(b) the magnitude of B,

(c) the angle between B and C.

2. John had a good long walk on Sunday morning with his dog. He started from his home walking 1.2 mile east, then 1.5 miles 30 degree N of E, followed by 2.0 miles, 45 degrees of S of W. At this point, what is his position with respect to his home?

Answer 1

Bu + 4 = Ay Bx+3 = Ax 121= √3²+42 - = 5 Ax=0 Ay=-65x2) - B x=-3 = -10 by = -14 Bx= -3, By =-14 magnitude of B = 14:32 angle angle between B and C is cos" (B.?) = cos 11-9-56 . (5x14.32 = 155.206°

1 N 10 5 15 _30 ing Alonge . Ry= led - 1. 5 cos 30° - 2 CO345° 10t sin 30° +(2 sin 45 X(-1))

Rx = -1.51 Ry = -0.66 direction = 64.08° south of west IR l = 1.65 mile

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