Question

Section 1.7 Vectors and Vector Addition 1.24 For the vectors A and Figure E1.24 B in Fig. E1.24, use a scale drawing to find the magnitude and direction of (a) the vector sum A + B and (b) the vector D (10.0 m) 30.0 difference A -B. Use your answers to find the magnitude and direction of (c) -A -B5 0 and (d) B -A. (See also Exercise 1.31 for a different approach.) 1.25A postal employee drives a delivery truck along the route shown in Fig. E1.25. Determine the magnitude and direc- tion of the resultant displacement by drawing a scale diagram. (See also Exercise 1.32 for a different approach.) B (15.0 m) 53.0 č12.0 m) A (8.00 m)

Answer 1

From the diagram we can express that

in meters

From the diagram we can express that A^vector = -8j^^in meters B^vector = 15 cos 60 i^^+ 15 sin 60 j^^(we take 90 - 30 = 60 degrees from + x axis) or B^vector = 7.5i^^+ 13j^^ Similarly C^vector = -12 cos 25i^^- 12 sin 25j^^ C^vector = -10.88i^^- 5.07j^^ and D^vector = -10 sin 53i^^+ 10 cos 53j^^ D^vector = -7.99i^^+ 6.02 j^^ Now, Part - a: A^vector + B^vector = (0 + 7.5)i^^+ (-8 + 13)j^^ which gives us A^vector + B^vector = 7.5 i^^+ 5j^^ The magnitude of the two vectors x and y is given byVertical-bar R Vertical-bar = squareroot x^2 + y^2 and the direction is given by theta = tan^-1 (y/x) Thus the magnitude of A^vector + B^vector isVertical-bar A^vector + B^vector Vertical-bar = squareroot (7.5)^2 + (5)^2 which gives usVertical-bar A^vector + B^vector Vertical-bar = 9.01 almostequalto 9 m and the direction is theta = tan^-1 (5/7.5) or theta = 33.7 almostequalto 34 degree with

(we take 90-30 = 60 degrees from +x axis)

or

Similarly

and

Now,

part-a

which gives us

The magnitude of the two vectors x and y is given by

and the direction is given by

Thus

the magnitude of   is

which gives us

and the direction is

or

Part-b

which gives us

Thus the magnitude will be

which give us

and the direction is

Part-c

thus

and the direction is

Part-d

and