If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate…
If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it
penetrate more before coming to rest?
1 cm
2 cm
3 cm
4 cm
Solution
Let the initial velocity of the body be v. Hence the final velocity = v/2
Applying $v^2=u^2-2 a s \Rightarrow\left(\frac{v}{2}\right)^2=v^2-2 \cdot a \cdot 3 \Rightarrow a=v^2 / 8$
In IInd case when the body comes to rest, final velocity = 0, initial velocity = v/2
Again, $(0)^2=\left(\frac{v}{2}\right)^2-2 \cdot \frac{v^2}{8} \cdot s ;$ or $s=1 \mathrm{~cm}$
So the extra penetration will be $1 \mathrm{~cm}$