Question

A bullet having a mass $10g$ is travelling horizontally with a velocity of $160m{{s}^{-1}}$ incident on a stationary wooden block and then it comes to rest in$0.02s$.The distance of penetration of the bullet into the block will be given as,
$\begin{aligned} & A.1.20m \\\ & B.1.60m \\\ & C.2.00m \\\ & D.2.40m \\\ \end{aligned}$

Answer 1

The basic equations of motion is to be used to solve this problem. First of all find out the acceleration using the equation,
$v=u+at$
And then find the displacement of the body using another equation of motion given as,
${{v}^{2}}={{u}^{2}}+2as$
These will help you to get into the answer correctly.

Complete answer:

It is already mentioned in the question that,
$\begin{aligned} & u=160m{{s}^{-1}} \\\ & t=0.02s \\\ \end{aligned}$
As the bullet is finally coming to rest, then the final velocity is given as,
$v=0m{{s}^{-1}}$
After substituting the terms in it, the equation can be written as,
$0=160+a\left( 0.02 \right)$
Therefore after rearranging the terms, the acceleration of body can be found out which is given as,
$a=-8000m{{s}^{-2}}$
Now let us substitute this terms in the final equation of motion which can be written as,
${{v}^{2}}={{u}^{2}}+2as$
Rearranging the equation in terms of the displacement of the object,
$s=\dfrac{{{v}^{2}}-{{u}^{2}}}{2a}$
Now let us substitute the values of terms in it,
$\begin{aligned} & s=\dfrac{0-{{160}^{2}}}{2\left( -8000 \right)} \\\ & s=\dfrac{-25600}{16000}=1.6m \\\ \end{aligned}$
Therefore the distance of the bullet penetrated into the block is obtained.

Hence the correct answer is option B.

Note:
The equations of motion are the basic equations that explain the nature of a mechanical system on the basis of its motion in terms of time. Specifically speaking, the equations of motion explains the behaviour of a physical system in the form of mathematical functions on the basis of dynamic variables. Uniform motion of a body is described as if a body travels in a straight line and traverses a similar amount of distance in a similar interval of time. The distance travelled is not equal in an equal interval of time is termed as non-uniform motion.