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

Step-by-step 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

Step-by-step 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=√(v_1^2+v_2^2)`

`v=√(24^2+11^2)`

v = 26.4 m

To find direction,

`\theta=tan^(-1)((v_2)/(v_1))`

`\theta=tan^(-1)((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.