1. Tardigrade
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  4. Let a bullet is fired into a wooden block and after penetrating 90cm into the block, the bullet loses half of its velocity. If the further distance travelled by the bullet before coming to the rest (in m ) is 0.3x then find x .

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Q. Let a bullet is fired into a wooden block and after penetrating $90cm$ into the block, the bullet loses half of its velocity. If the further distance travelled by the bullet before coming to the rest (in $m$ ) is $0.3x$ then find $x$ .

NTA AbhyasNTA Abhyas 2022

Solution:

Using $v^{2}-u^{2}=2as_{1}$
$\left(\frac{u}{2}\right)^{2}-u^{2}=2as_{1}$
$\Rightarrow a=\frac{- 3 u^{2}}{8 s_{1}}$
For $2^{\text{nd }}$ part of motion,
$\left(0-\left(\frac{u}{2}\right)^{2}=2 \quad as _{2}\right.$
Substituting for $'a'$ we get,
$s_{2}=\frac{s_{1}}{3}=\frac{90}{3}cm=30cm=0.3m$