Question

Need detail information in how to approach this problem. Im having a bad time and i would love to get some help

For the vectors A and B in Fig. E1.24, use a scale drawing to find the magnitude and direction of (a) the vector sumAB and (b) the vector difference À - B. Use your answers to find the magnitude and direction of (c)-A - B and (d) B- A. (See also Exercise 1.31 for a different approach.) Figure E1.24 y B (15.0 m) 30.0 D (10.0 m) 53.0 25.0 Č(12.0 m) A (8.00 m) 1.31 For the vectors A and B in Fig. E1.24, use the method of components to find the magnitude and direction of (a) the vector sum A + B; (b) the vector sum B + A; (c) the vector difference A -B (d) the vector difference B - A

Answer 1

Given that,

$\vec{A}$ = -8 j

$\vec{B}$ = 15 sin 30 i + 15 cos 30 j = 7.5 i + 13 j

(a)

Vector sum, $\vec{A}$ + $\vec{B}$ =  -8 j + (7.5 i + 13 j)

$\vec{A}$ + $\vec{B}$ = 7.5 i + 5 j

magnitude, |$\vec{A}$ + $\vec{B}$ | = sqrt (7.5² + 5²)

|$\vec{A}$ + $\vec{B}$ | = 9 m

Direction , $\theta$ = tan^-1 (5 / 7.5)

$\theta$ = 33.7 deg

(b)

Vector sum, $\vec{B}$ + $\vec{A}$ = 7.5 i + 13 j + (-8 j)

$\vec{B}$ + $\vec{A}$ = 7.5 i + 5 j

magnitude, |$\vec{B}$ + $\vec{A}$ | = sqrt (7.5² + 5²)

|$\vec{B}$ + $\vec{A}$ | = 9 m

Direction , $\theta$ = tan^-1 (5 / 7.5)

$\theta$ = 33.7 deg

(c)

$\vec{A}$ - $\vec{B}$ =  -8 j - (7.5 i + 13 j)

$\vec{A}$ - $\vec{B}$ = -7.5 i - 21 j

magnitude, |$\vec{A}$ - $\vec{B}$ | = sqrt [(-7.5)² + (-21)²]

|$\vec{A}$ - $\vec{B}$ | = 22.3 m

Direction,  $\theta$ = 180 + tan^-1 (-21 / -7.5)

$\theta$ = 180 + 70.3 deg

$\theta$ = 250.3 deg

(d)

Vector difference, $\vec{B}$ - $\vec{A}$ =  (7.5 i + 13 j) - (-8 j)

$\vec{B}$ - $\vec{A}$ = 7.5 i + 21 j

Magnitude,  |$\vec{B}$ - $\vec{A}$ | = 7.5^2 + 21^2

|$\vec{B}$ - $\vec{A}$ | = 22.3 m

Direction,  $\theta$ = tan^-1 (21 / 7.5)

$\theta$ = 70.3 deg