Respuesta :
Answer:
The magnitude of resultant vector and direction are 1.843 m and 77.47° east of north.
Explanation:
Given that,
Magnitude of displacement due to east = 2.8 km
Magnitude of displacement due to north = 2.8 km
Magnitude of displacement due to west = 2.4 km
Magnitude of displacement due to south = 1 km
We need to calculate the resultant of the displacement
[tex]D = d_{1}+d_{2}+d_{3}+d_{4}[/tex]
[tex]D=2.8\hat{i}+2.8\hat{j}-2.4\hat{i}-1\hat{j}[/tex]
[tex]D=0.4\hat{i}+1.8\hat{j}[/tex]
The magnitude of the resultant vector
[tex]D=\sqrt{(0.4)^2+(1.8)^2}[/tex]
[tex]D=1.843\ m[/tex]
We need to calculate the direction
Using formula of direction
[tex]\tan\theta=\dfrac{j}{i}[/tex]
Put the value into the formula
[tex]\tan\theta=\dfrac{1.8}{0.4}[/tex]
[tex]\theta=\tan^{-1}4.5[/tex]
[tex]\theta=77.47^{\circ}[/tex]
Hence, The magnitude of resultant vector and direction are 1.843 m and 77.47° east of north.
