Question

If a bullet loses $10\%$ speed while moving through a plank, then find the minimum number of planks required to stop the bullet.

Answer 1

Energy losses in one plank $=\frac{1}{2}m[v^2-(0.9v{)}^2]$

$=\frac{1}{2}m[v^2-0.81v^2]$

$=\frac{1}{2}m\left(0.19r^2\right)$

Now no. of plank required to stop the bullet $=\frac{\frac{1}{2}m{v}^2}{\frac{1}{2}m\left(0.19v^2\right)}=\frac{1}{0.19}=5.26\cong 6$ planks