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  4. If a body loses half of its velocity on penetrating 3 cm in a wooden block then how much will it penetrate more before coming to rest?

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Q. If a body loses half of its velocity on penetrating 3 cm in a wooden block then how much will it penetrate more before coming to rest?

MGIMS WardhaMGIMS Wardha 2011

Solution:

Let initial velocity of body at point A is v. AB is 3 cm $ {{v}^{2}}={{u}^{2}}-2as $ $ {{\left( \frac{v}{2} \right)}^{2}}={{v}^{2}}-2a\times 3 $ $ a=\frac{{{v}^{2}}}{8} $ Let an penetrating 3 cm in a wooden block the body moves $ x $ distance from B to C According to the question $ u=\frac{v}{2} $ and $ v=0 $ $ \therefore $ $ {{(0)}^{2}}={{\left( \frac{v}{2} \right)}^{2}}-2\times \frac{{{v}^{2}}}{8}\times x $