A bomb of 1kg is thrown vertically up at a speed 100m/sec. After 5 seconds it explodes into two parts. One of the mass 400 grams goes down at a speed of 25m/sec. What is the speed and direction of the other part just after the explosion?

after 5sec velocity of bomb:

$\mathrm{v}=\mathrm{u}-\mathrm{gt}=100-10\times 5=50\mathrm{m}/\sec$

Mass of one piece of bomb = 400 grams = 0.4 kg

Mass of second piece of bomb = 1000- 400 = 600 grams = 0.6 kg

Initial momentum before the explosion:

= mv

$=1\times 50 \mathrm{kgm}{\sec }^{-1}$

From momentum conservation

$1\times 50=-0.4\times 25+0.6{\mathrm{V}}^{|}$

${\mathrm{V}}^{|}=100 \mathrm{m}/\sec$ upwards