A bullet of mass m and velocity vo is fired toward a block of mass 4m. The block is initially at rest on a fri

A bullet of mass m and velocity vo is fired
toward a block of mass 4m. The block is
initially at rest on a frictionless horizontal
surface. The bullet penetrates the block and
emerges with a velocity of vo /3.
a. Determine the final speed of the block.
b. Determine the loss in kinetic energy of the bullet.
c. Determine the gain in the kinetic energy of the block

By conservation of momentum

mV0 = 4m (Vb) + mV0/3
V0 = 4 (Vb) + V0/3
Vb = V0/6 Answer for a .
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Loss of energy of bullet = 0.5 *m (V0² - V0²/9) = (4/9) mV0² Answer for b

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gain in the kinetic energy of the block 0.5*4m* (V0/6 ) ² = (1/18 )mV0² ---------Answer for c
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