Question

A bullet is fired at a target with a velocity 80 m/s and penetrates 50 cm into it. If this bullet were fired into a target 25 cm thick with equal velocity, with what velocity would it emerge, supposing the resistance to be uniform and the same in both the cases?

• A. $\sqrt{80}m/s$
• B. $\frac{40}{\sqrt{2}}m/s$
• C. $40m/s$
• D. $40\sqrt{2}m/s$

Answer 1

The correct option is D $40\sqrt{2}m/s$

In the first case the initial velocity(u) = 80 m/s and distance travelled(s) = 50 cm.

But, here the final velocity $=0$, thus

$0=u^2-2as$ ( negative sign because some resistive force is acting )

$a=6400m/s^2$

In the second case case acceleration $\left(a\right)=6400m/s^2$

Substituting in equation, we have

$v_1^2=u_1^2-2a{s}_1$

$=(80{)}^2-2\times 6400\times \frac{1}{4}$

$=6400-3200$

$=3200$ or $v_1=40\sqrt{2}$

The emerging velocity is $40\sqrt{2}m/s$.