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in Physics by (62.3k points)

A 50 g bullet moving horizontally with a velocity of 300 ms-1 hits and remains embedded in a block of wood, weighing 10 kg and suspended by a long rope. Through what vertical height the block of the wood is being caused to rise by the bullet? (g = 9.8 ms-2)

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Momentum of the bullet and block before impact = 50 x 10-3 x 300 = 15 Ns

If v the velocity of a system (bullet and block) after collision, then by the conservation law of momentum, 15 = (10 + 0.05)v

or, v = {15}/{10.05} = 300/201 ms-1

and the height raised by the system,

h = v2/2g = {(300/201)2}/{2 x 9.8} = 0.1136 m

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