A $0.15 \; kg$ glider is moving to the right on a friction less horizontal air track with a speed of $0.8 \; m/s$. It has a ahead on collision with a $0.3 \; kg$ glider that is moving to the left with a speed of $2.2 \; m/s$. Find the final velocity (magnitude and direction) of each glider if the collision is elastic.

Given,

Mass of glider $(M_1) = 0.15\;kg$

Mass of glider $M_2 = 0.3\;kg$

Initial velocity $u_1 = 0.8\;m/s$               [moving to the right]

Initial velocity $u_2 = -\;2.2\;m/s$            [moving to the left]

Final velocity $v_1 = ?$

Final velocity $v_2 = ?$

From the principle of conservation of linear momentum, we have

$M_1\;u_1 + M_2\;u_2 = M_1\;v_1 + M_2\;v_2$

or, $0.15 * 0.8 + 0.3 * (-2.2) = 1.15\;v_1 + 0.3\;v_2$

or, $-0.54 = 0.15\;v_1 + 0.3\;v_2$ .......... (i)

From the question, we know that it is elastic collision.

So, for the elastic collision,

$u_1 + v_1 = u_2 + v_2$

or, $0.8 + v_1 = -\;2.2 + v_2$

or, $v_1 - v_2 = -\;3$ .......... (ii)

Solving equation (i) and (ii), we get

∴ $v_2 = -\;0.2\;m/s$

∴ $v_1 = -\;3.2\;m/s$

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