Question

Consider two vectors A~ and B~ and their resultant A~ + B~ . The magnitudes of the vectors A~ and B~ are, respectively, 15 and 7.3 and they act at 86◦ to each other. A~ B~ A~ + B~ Find the magnitude of the resultant vector A~ + B~ . 005 (part 2 of 2) 4.0 points Find the angle between the direction of the resultant vector A + B and the direction of the vector A. Answer in units of ◦ .

Answer 1

Answer:

17.13 ,1.31°

Explanation:

Magnitude of vector A = 15

Magnitude of vector B = 7.3

Angle between A and B is θ = 86°

Let the magnitude of the resultant is R.

use the formula for the resultant of two vectors

$R=\sqrt{A^{2}+B^{2}+2ABCos\theta$

$R=\sqrt{15^{2}+7.3^{2}+2\times15\times7.3Cos86 }$

R = 17.13

Let the angle between A and R is α.

$tan\alpha =\frac{BCos\theta }{A+BSin\theta }$

$tan\alpha =\frac{7.3Cos86 }{15+7.3Sin86 }$

tan α = 0.02286

α = 1.31°