Question

show graphically the displacement vector for a motion in two dimension.write an expression for displacement vector in terms of it's rectangular components
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Answer 1

Given:

The motion is in two dimension.

To Show:

Displacement vector for a motion in two dimension. And displacement vector in terms of its rectangular components.

Solution:

Let, a body moves from Q to P in the path AB as shown in the graph and let the displacement vector be R.

∴ From the graph,

Displacement vector, R = Position vector of P (OP) - Position vector of Q    

                                                                                         (OQ)

(*Graph is attached below)

Now, let R makes an angle $\theta$ with x-axis, then its rectangular components be like,

$R_x = |\bold{R}|\cos \theta$    ...(1)

$R_y = |\bold{R}|\sin \theta$    ...(2)

Now, squaring and adding equation (1) and (2) we get,

$|\bold{R}|^2=R_x^2+R_y^2$      (∵$\cos^2\theta+\sin^2\theta=1$)

$=>|\bold{R}|=\sqrt{R_x^2+R_y^2}$