Answer:
(v, 0) or (0, v)
Explanation:
The law of conservation of linear momentum states total initial momentum equal total final momentum.
Total initial momentum = [tex]mv + m\times 0 = mv[/tex]
Total final momentum = [tex]mv_1 + mv_2 = m(v_1+v_2)[/tex]
Equating both,
[tex]mv = m(v_1+v_2)[/tex]
[tex]v = v_1+v_2[/tex]
For an elastic collision, kinetic energy is conserved i.e. total initial kinetic energy = total final kinetic energy
[tex]\frac{1}{2}mv^2 + \frac{1}{2}m\times0^2 = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2[/tex]
[tex]v^2 = v_1^2+v_2^2[/tex]
From the first equation, [tex]v_1 = v-v_2[/tex].
Substituting this in the second equation,
[tex]v^2 = (v-v_2)^2+v_2^2[/tex]
[tex]v^2 = v^2-2vv_2 +v_2^2+v_2^2[/tex]
[tex]0 = 2v_2^2-2vv_2[/tex]
[tex]v_2(v_2-v) = 0[/tex]
[tex]v_2 = 0[/tex] or [tex]v_2 = v[/tex]
From [tex]v_1 = v-v_2[/tex],
[tex]v_1 = v-v = 0[/tex]
OR
[tex]v_1 = v-0 = v[/tex]
