Explanation

(b) [image:6_image89.png]
Let the thickness of each plank is $s$. If the initial speed of bullet is $100\ m/s$ then it stops by covering a distance $2s$
By applying $v^{2} = u^{2} - 2as \Rightarrow 0 = u^{2} - 2as$
$s = \frac{u^{2}}{2a}\ s \propto u^{2}$ [If retardation is constant]
If the speed of the bullet is doubled then bullet will cover four times distance before coming to rest
$i.e.$ $s_{2} = 4\left( s_{1} \right) = 4(2s) \Rightarrow s_{2} = 8s$
So number of planks required $= 8$