Question

Vector 1 has a magnitude of 24 m and is pointed to the west. Vector 2 has a magnitude of 11 and is pointed to the north. What is the magnitude and direction of the resultant vector produced by these two?

Answer 1

Answer:

Explanation:

A = 24 m west

B = 11 m north

Write these in vector form

$\overrightarrow{A}= - 24\widehat{i}$

$\overrightarrow{B}= 11\widehat{j}$

Resultant of two vectors is

$\overrightarrow{R} = \overrightarrow{A} + \overrightarrow{B}$

$\overrightarrow{R}= - 24 \widehat{i} + 11\widehat{j}$

Magnitude of resultant

$R=\sqrt{24^{2}+11^{2}}$

R = 26.4 m

Direction

tan θ =  - 11 / 24

θ = - 24.6°

Answer 2

Explanation:

It is given that,

Vector 1 has a magnitude of 24 m and is pointed to the west.

Vector 2 has a magnitude of 11 and is pointed to the north.

Let v is the resultant of two vectors. The resultant of two vectors is given by :

$v=\sqrt{v_1^2+v_2^2}$

$v=\sqrt{24^2+11^2}$

v = 26.4 m

To find direction,

$\theta=tan^{-1}(\dfrac{v_2}{v_1})$

$\theta=tan^{-1}(\dfrac{11}{24})$

$\theta=24.62^{\circ}$

So, the magnitude and direction of the resultant vector produced by these two is 26.4 m and 24.62 degrees respectively. Hence, this is the required solution.