Question

A bullet leaves a rifle with a velocity of 200 m/s and strikes a wooden target up to 4 cm. What velocity should it have to pierce the same block of wood up to 16 cm?

Answer 1

Step 1: given data

Velocity is $v=200m/s$

Distance is $S=4cm=0.04metres$

Step 2: calculating force

For the given case, Kinetic energy = Work done

Kinetic energy is given by,

$KE=\frac{1}{2}m{v}^2$

where, $m$ is mass and $v$ is velocity.

Work done is given by,

$W=FS$

where, $F$ is force and $S$ is displacement.

Now, according to the question,

$\begin{array}{l}KE=W\\ \frac{1}{2}m{v}^2=FS\end{array}$

Substituting the known values, we get,

$\begin{array}{l}\frac{1}{2}m{(200metres/sec)}^2=F\left(0.04metres\right)\\ \frac{m\times 40000}{2}=0.04F\\ F=\frac{20000m}{0.04}\\ F=500000mN\end{array}$

Step 3: calculating velocity for the new distance

Now, when $S=16cm=0.16metres$, velocity can be calculated as follows:

$\begin{array}{l}KE=W\\ \frac{1}{2}m{v}^2=FS\end{array}$

Substituting the value for $S$ and $F$ in the above equation, we get,

$\begin{array}{l}\frac{1}{2}m{v}^2=\left(500000mN\right)\left(0.16metres\right)\\ v^2=\frac{2\left(500000m\right)\left(0.16\right)}{m}\\ v^2=160000\\ v=\sqrt{160000}\\ v=400m/s\end{array}$

Therefore, the velocity at which the bullet should hit the same block in order to pierce the wood up to 16 cm is $400m/s$.