a
(a)Velocity of \(50 \,kg\). mass after \(5 \,sec \) of projection \(v = u - gt\)\( = 100 - 9.8 \times 5 = 51\;m/s\)
At this instant momentum of body is in upward direction
\({P_{{\rm{initial}}}} = 50 \times 51 = 2550\;kg - m/s\)
After breaking \(20\, kg\) piece travels upwards with \(150 \,m/s\) let the speed of \(30 \,kg\) mass is \(V\)
\({P_{{\rm{final}}}} = 20 \times 150 + 30 \times V\)
By the law of conservation of momentum
\({P_{{\rm{initial }}}} = {P_{{\rm{final}}}}\)
==> \(2500 = 20 \times 150 + 30 \times V \Rightarrow V = - 15\;m/s\)
i.e. it moves in downward direction.