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Question

A bullet hits a wooden block and loses half its velocity after penetrating 3cm. How much more will it penetrate before coming to rest?
Can we Solve this with work energy theorem?

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Solution

Let bullet be fired at velocity v . Given that velocity decreases to half after penetrating 3 cm i.e. when v becomes v/2 .
let s be distance travelled by bullet through 3 cm. Let F be retarding force offered by target.
Acc to work energy theorem, we can write kinetic energy as :
1 half straight m open parentheses straight v over 2 close parentheses squared minus space 1 half mv squared equals space minus space straight F. straight s space space space space space space space 1 half mv squared equals 4 over 3 straight F. straight s space space space....... left parenthesis 1 right parenthesis let space straight s space be space distance space travelled Acc space to space work space energy space theorem comma space 1 half cross times straight m cross times 0 squared minus space 1 half mv squared equals negative space straight F. straight s apostrophe 1 half mv squared equals straight F. straight s apostrophe space space space space space...... left parenthesis 2 right parenthesis from space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis space 4 over 3 straight F. straight s equals straight F. straight s apostrophe straight s apostrophe equals 4 over 3 straight s here space straight s equals space 3 space cm straight s apostrophe equals 4 over 3 cross times 3 straight s apostrophe equals 4 space cm so space additional space thickness space bullet space will space penetrate space before space coming space to space rest space is 4 space minus 3 equals space 1 space cm

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