b
(b)Let the velocity of third part after explosion is\(  V\)
After explosion momentum of system = \({\vec P_1} + {\vec P_2} + {\vec P_3}\)
= \(\frac{m}{3} \times 100\hat j - \frac{m}{3} \times 100\hat j + \frac{m}{3} \times V\hat i\)
By comparing momentum of system before and after the explosion
\(\frac{m}{3} \times 100\hat j - \frac{m}{3} \times 100\hat j + \frac{m}{3}V\hat i = 100m\hat i\)

==>\(V = 300\,m/s\)