Question

The velocity of a bullet is 200ms¹ and it can penetrate a plank of thickness 0.03m. What will be the velocity of the bullet if it can penetrate 0.12m plank?

Answer 1

Explanations & Calculations

• The energy conversion associated with this process is the kinetic energy the bullet has before hitting the plank is being expended to the work against the friction applied by the plank.

$\qquad\qquad\qquad\qquad\qquad\small KE = fs$

• Since the friction force from the plank as well as the mass of the bullet is not given, they are the points of this sum to be carefully thought of.
• We need to consider the planks being equal in their properties and the same bullet is used so that $\small f$ and $\small m$ can be treated as the same values throughout the sum.
• Writing the energy conversion to both incidents & then dividing appropriately, gives the answer needed.

$\qquad\qquad \begin{aligned} \small \frac{1}{2}mv^2&=\small fs\\ \small \frac{m(200\,ms^{-1})^2}{2}&=\small f(0.03\,m)\cdots\cdots(1)\\ \\ \small \frac{m(v)^2}{2}&=\small f(0.12\,m)\cdots\cdots(2)\\ \\ \small (2) \div (1),\\ \\ \small \frac{v^2}{(200\,ms^{-1})^2}&=\small \frac{0.12\,m}{0.03\,m}\\ \small v^2&=\small 160000\,m^2s^{-2}\\ \small \bold{v}&=\small \bold{400\,ms^{-1}} \end{aligned}$