A particle take the following successive displacement 10km south west, 50 KM north of East. Find the magnitude of the resistant

Answer 1

To find the magnitude of the resultant displacement, we can use the Pythagorean theorem.

Let's call the displacement in the South-West direction as A and the displacement in the North-East direction as B.
The magnitude of the resultant displacement (R) can be found using the formula:

R^2 = A^2 + B^2

The displacement of 10km in the South-West direction can be split into two components: 10km towards the south and 10km towards the west. The displacement of 50km in the North-East direction can be split into two components: 50km towards the north and 50km towards the east.

So, A = 10km + 50km (towards west)
= 10km + (-50km)
= -40km (towards west)

B = 50km + 10km (towards north)
= 60km (towards north)

Now, substituting the values in the formula, we get:

R^2 = (-40km)^2 + (60km)^2
R^2 = 1600km^2 + 3600km^2
R^2 = 5200km^2

Taking the square root of both sides, we get:

R = sqrt(5200km^2)
R ≈ 72.11km

Therefore, the magnitude of the resultant displacement is approximately 72.11km.