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Answer to Question #26243 in Mechanics | Relativity for thakshi

Question #26243
A bullet, when fire at a fixed target, has its speed decreased to 50% after penetrating 15cm in to it. What additional thickness it will penetrate before coming to rest?
Expert's answer
A bullet, when fire at a fixed target, has its speed decreased to 50%
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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