Question

A bullet moving with a speed of $150$ $m{s}^{-1}$, strikes a wooden plank. After passing through the plank, its speed becomes $125$ $m{s}^{-1}$. Another bullet of the same mass and size strikes the plank with a speed of $90$ $m{s}^{-1}$. Its speed after passing through the plank would be.

• A. $25$ $m{s}^{-1}$
• B. $35$ $m{s}^{-1}$
• C. $50$ $m{s}^{-1}$
• D. $70$ $m{s}^{-1}$

Answer 1

Answer: (B)

$35$ $m{s}^{-1}$

Let the magnitude of retardation of the bullet during striking be $a$.

Here, since retardation is taking place, we take $-a$ instead of $a$ in the equation

Using, the third equation of motion,

$v^2=u^2+2as$,

For the first bullet, we have $u=150m/s,v=125m/s$

$\Rightarrow {125}^2={150}^2-2as$

$\Rightarrow 2as=6875$ ( Where $s$ is size of plank , same for both)

For the second bullet, given $u=90m/s$

Let speed $v$ after passing through the plank.

$\Rightarrow v^2={90}^2-2as$

$\Rightarrow v^2=8100-6875=1225$

$\Rightarrow v=35m{s}^{-1}$