Answer to Question #26243 in Mechanics | Relativity for thakshi
after penetrating 15cm in to it. What additional thickness it will
penetrate before coming to rest?
Let the velocity of a bullet was V before hitting target. Then the kinetic energy of a bullet was
K1 = mV²/2.
As after penetrating 15cm into a target bullet's speed decreased to 50%, its kinetic energy became
K2 = m(V/2)²/2 = mV²/8.
Assuming that the bullet's energy decreases linearly while penetrating a target. Then the amount of energy needed to penetrate one cm of a target is
E = (K1 - K2)/15 = (mV²/2 - mV²/8)/15 = mV²/40.
Therefore the bullet will penetrate
D = K2/E = (mV²/8) / (mV²/40) = 5 [cm]
more before coming to rest.
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