Answer
64.8k+ views
Hint: In order to solve this question, the concept of energy conservation is important. Here initial energy of the bullet is given and also the energy lost when the bullet hits the soft plywood is also given. The formula of Kinetic energy contains the velocity in it. Hence, for calculating the emergent speed of velocity use the concept of kinetic energy.
Formula Used:
Kinetic Energy is given by,
$KE = \dfrac{1}{2}m{v^2}$
Here, $m$ is the mass of the object.
$v$ is the velocity of the object.
Complete step by step answer:
Here we are given that,
Mass of the bullet fired by Abhijeet = \[100g\]
Initial speed or velocity of the bullet when it is fired = $100m{s^{ - 1}}$
Now, it is given in the question that the bullet emerges with only the $10\% $ of its initial Kinetic Energy. So we have,
Final Kinetic Energy = $10\% $ of Initial Kinetic Energy
This can also be written as,
Final Kinetic Energy = $0.1$ $ \times $ Initial Kinetic Energy
As we know that, Kinetic Energy is represented by the expression,
$KE = \dfrac{1}{2}m{v^2}$
Here, $m$ is the mass of the object which in this case is bullet.
$v$ is the velocity of the object.
Let the final velocity of the bullet when it emerges from the soft plywood = ${v_f}$
Now putting the expression for kinetic energy in the equation, Final Kinetic Energy = $0.1$ $ \times $ Initial Kinetic Energy
We have,
$\dfrac{1}{2}mv_f^2 = 0.1 \times \dfrac{1}{2} \times m \times {(100m{s^{ - 1}})^2}$
As mass $m$ is same on both the sides we can cancel it, also $\dfrac{1}{2}$ is same on both sides it will also be cancelled, so we have,
$v_f^2 = 0.1 \times 10000$
On solving the RHS we get,
$v_f^2 = 1000$
After taking square root we have,
${v_f} = 31.62m{s^{ - 1}}$
Hence the emergent speed is $31.62m{s^{ - 1}}$.
Note: Here in the above question we have used speed and velocity interchangeably yet these two the different physical quantities, the reason is that the magnitude of both speed and velocity is the same. The difference is that speed is a scalar quantity but velocity is a vector quantity. Velocity in simple terms is speed with direction.
Formula Used:
Kinetic Energy is given by,
$KE = \dfrac{1}{2}m{v^2}$
Here, $m$ is the mass of the object.
$v$ is the velocity of the object.
Complete step by step answer:
Here we are given that,
Mass of the bullet fired by Abhijeet = \[100g\]
Initial speed or velocity of the bullet when it is fired = $100m{s^{ - 1}}$
Now, it is given in the question that the bullet emerges with only the $10\% $ of its initial Kinetic Energy. So we have,
Final Kinetic Energy = $10\% $ of Initial Kinetic Energy
This can also be written as,
Final Kinetic Energy = $0.1$ $ \times $ Initial Kinetic Energy
As we know that, Kinetic Energy is represented by the expression,
$KE = \dfrac{1}{2}m{v^2}$
Here, $m$ is the mass of the object which in this case is bullet.
$v$ is the velocity of the object.
Let the final velocity of the bullet when it emerges from the soft plywood = ${v_f}$
Now putting the expression for kinetic energy in the equation, Final Kinetic Energy = $0.1$ $ \times $ Initial Kinetic Energy
We have,
$\dfrac{1}{2}mv_f^2 = 0.1 \times \dfrac{1}{2} \times m \times {(100m{s^{ - 1}})^2}$
As mass $m$ is same on both the sides we can cancel it, also $\dfrac{1}{2}$ is same on both sides it will also be cancelled, so we have,
$v_f^2 = 0.1 \times 10000$
On solving the RHS we get,
$v_f^2 = 1000$
After taking square root we have,
${v_f} = 31.62m{s^{ - 1}}$
Hence the emergent speed is $31.62m{s^{ - 1}}$.
Note: Here in the above question we have used speed and velocity interchangeably yet these two the different physical quantities, the reason is that the magnitude of both speed and velocity is the same. The difference is that speed is a scalar quantity but velocity is a vector quantity. Velocity in simple terms is speed with direction.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)