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  4. The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4+ x ) cm inside the block. The value of x is:

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Q. The velocity of the bullet becomes one third after it penetrates $4 cm$ in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at $(4+ x ) cm$ inside the block. The value of $x$ is:

JEE MainJEE Main 2022Laws of Motion

Solution:

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$ \left(\frac{ V }{3}\right)^2- V ^2-2 a (4) \Rightarrow a -\frac{8 V ^2}{9(8)}-\frac{ V ^2}{9}$
$ 0= V ^2-2 a (4+ x ) $
$ \Rightarrow V ^2=2\left(\frac{ V ^2}{9}\right)(4+ x )$
$ 4.5=4+ x $
$ x =0.5$