Question

Displacement vector points due east and has a magnitude of 2.8 km. Displacement vector points due north and has a magnitude of 2.8 km. Displacement vector points due west and has a magnitude of 2.4 km. Displacement vector points due south and has a magnitude of 1 km. Find the magnitude and direction (relative to due east) of the resultant vector + + + .

Answer 1

The magnitude of resultant vector and direction are 1.843 m and 77.47° east of north.

Step-by-step 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

`D = d_(1)+d_(2)+d_(3)+d_(4)`

`D=2.8\hat{i}+2.8\hat{j}-2.4\hat{i}-1\hat{j}`

`D=0.4\hat{i}+1.8\hat{j}`

The magnitude of the resultant vector

`D=√((0.4)^2+(1.8)^2)`

`D=1.843\ m`

We need to calculate the direction

Using formula of direction

`\tan\theta=(j)/(i)`

Put the value into the formula

`\tan\theta=(1.8)/(0.4)`

`\theta=\tan^(-1)4.5`

`\theta=77.47^(\circ)`

Hence, The magnitude of resultant vector and direction are 1.843 m and 77.47° east of north.