Question

A bullet of mass $5g$ travels with a speed of $500m{s}^{-1}.$ if it penetrates a fixed target which offers a constant resistive force of 1000 N to the motion of the bullet, find :
(a) the initial kinetic energy of the bullet,
(b) the distance through which the bullet has penetrated.

• A. $s=0.625m$
• B. $s=0.725m$
• C. $s=0.225m$
• D. $s=0.65m$

Answer 1

The correct option is A $s=0.625m$

Given,

$mass=5g$

$speed=500m/s$

$force=1000N$

(a) kinetic energy$=\frac{1}{2}\times m\times v\times v$

$m=5g=\frac{5}{1000}kg$

$v=500$

$\Rightarrow \frac{1}{2}\times \frac{5}{1000}\times 500\times 500$

=$625J$

(b) $force=mass\times acceleration$

$1000=\frac{5}{1000}\times acceleration$

Acceleration$=1000\times \frac{1000}{5}$

=$200000m/s^2$

using the third equation of motion

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

$(500{)}^2=0+2\times 200000\times s$

$250000=400000\times s$

$s=0.625m$