Question

A vector A makes an angle of 20 degree and B makes an angle of 110 degree with the x-axis. The magnitude of this vectors are 3 m and 4 m respectively. find the resultant and direction​

Answer 1

The resultant is 5 m at $73.1^{\circ}$

Explanation:

To solve the problem, we have to resolve each of the two vectors into its component along the x-axis and the y-axis.

Vector A has magnitude 3 m and angle 20 degrees with the x-axis, so its components are

$A_x = A cos \theta = (3)(cos 20)=2.82 m$

$A_y = A sin \theta = (3)(sin 20)=1.03 m$

Vector B has magnitude 4 m and angle 110 degrees, so its components are

$B_x = B cos \theta = (4)(cos 110)=-1.37 m$

$B_y = B sin \theta = (4)(sin 110)=3.76 m$

So, the x- and y- components of the resultant vector are

$R_x = A_x + B_x = 2.82+(-1.37)=1.45 m\\R_y = A_y+B_y = 1.03+3.76 =4.79 m$

Therefore the magnitude of the resultant is

$R=\sqrt{R_x^2+R_y^2}=\sqrt{(1.45)^2+(4.79)^2}=5.0 m$

While the direction is given by

$\theta=tan^{-1}(\frac{R_y}{R_x})=tan^{-1}(\frac{4.79}{1.45})=73.1^{\circ}$

Learn more about resultant of two vectors:

brainly.com/question/4945130

brainly.com/question/5892298

#LearnwithBrainly