A bullet having a mass of $10$ g and moving with a speed of $1.5$ m/s, penetrates a thick wooden plank of mass $90$ g. The plank was initially at rest. The bullet gets embedded in the plank and both move together. Determine their velocity.

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Solution

mass of bullet $= 10 g = 0.01 k g$
velocity of bullet $= 1.5 \frac{m}{s}$
mass of plank $= 90 g = 0.09 k g$
Total momentum before collision=mass $\times$ velocity
$= 0.01 \times 1.5 + 0.09 \times 0 = 0.015 k g \frac{m}{s}$
Total momentum after collision=(mass of bullet +mass of plank ) $\times$ velocity
$= 0.1 k g \times V = 0.1 V k g \frac{m}{s}$
According to law of conservation of momentum,
Total momentum before collision=Total momentum after collision
$0.015 k g \frac{m}{s} = 0.1 v k g \frac{m}{s}$
velocity acquired by theplank and the bullet $= 0.15 \frac{m}{s}$

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