Answer
The correct answer is:
(b) Direction of vector 2 and magnitude $\sqrt{2}~v$
Work Step by Step
The initial momentum of the system is zero. By conservation of momentum, the final momentum of the system must also be zero.
After the explosion:
$m~v_1+m~v_2+m~v_3 = 0$
$m~v_3 = -(m~v_1+m~v_2)$
$v_3 = -(v_1+v_2)$
The velocity of the third fragment is the negative of the vector sum of the other two fragments. The vector sum of the first two fragments has a magnitude of $\sqrt{2}~v$ in the +x-direction. Therefore, the velocity of the third piece has a magnitude of $\sqrt{2}~v$ in the -x-direction.
The correct answer is:
(b) Direction of vector 2 and magnitude $\sqrt{2}~v$
