Question

A bullet is fired on a fixed target. It penetrates inside the target through distance $d=3.75$ cm and then stops, mass of the bullet is $m=1$ kg and of the target is $M=4$ kg. Now an identical bullet moving with the same velocity is fired on the identical target which is placed at rest on a frictionless horizontal surface. Then find the distance (in cm) to which the bullet will penetrate inside the target?

Answer 1

Let, F be the thrust force .
Case (i);when the block is fixed,

$v^2=2\frac{F}{m}s=2\frac{F}{m}\left(3.75\right)$

$\Rightarrow \frac{v^2}{2F}=3.75$----->(a)

Case(ii): when the block is placed on a smooth plane,
in this case, thrust force gives velocity to block and decelerates bullet.

let, $s_1$ be the distance travelled by the bullet and $s_2$ is the distance travelled by block.

$s_1=v^{2}t-\frac{1}{2}\frac{F}{1}{t}^2$----->(1)

$s_2=\frac{1}{2}\frac{F}{4}{t}^2$------------->(2)

using,
v=u+at

$\frac{F}{4}t=v-\frac{F}{1}t$

$\Rightarrow t=\frac{4v}{5F}$

substitute above result in (1) and (2).we get,

$s_1=\frac{12v^2}{25F}$

and $s_2=\frac{2v^2}{25F}$

distance to which bullet penetrate=$s_1-s_2$

=$\frac{2v^2}{5F}$

=3 cm. { from (a)}