Question

Vector has magnitude of 5.0 m and it is directed east. Vector has magnitude of 4.0 m and is directed 30o west of north. What are the magnitude and direction of the vector ?

Answer 1

4.58 m, θ = 49 degree

Step-by-step explanation:

Vector 1

A = 5 m East

Vector 2

B = 4 m towards 30 degree west of north

write down the vectors in vector form

`\overrightarrow{A}=5\widehat{i}`

`\overrightarrow{B}=4\left (-Sin30\widehat{i}+Cos30\widehat{j}  \right )`
`\overrightarrow{B}=\left (-2\widehat{i}+3.464\widehat{j}  \right )`

The resultant of these two vectors is

`\overrightarrow{A}+\overrightarrow{B}=5\widehat{i}+\left (-2\widehat{i}+3.464\widehat{j}  \right )`

`\overrightarrow{A}+\overrightarrow{B}=3\widehat{i}+3.464\widehat{j}`

The magnitude of the resultant is given by

`=\sqrt{3^(2)+3.464^(2)}=4.58 m`

Let the resultant vector makes an angle θ from X axis

So,

`tan\theta =(3.464)/(3)=1.155`

θ = 49 degree