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A bullet on penetrating 30 cm into its target loses its velocity by 50%. What additional distance will it penetrate into the target before it comes to rest?
- a)30 cm
- b)20 cm
- c)10 cm
- d)5 cm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A bullet on penetrating 30 cm into its target loses its velocity by 50...
From (1) and (2) s = 10 m
Most Upvoted Answer
A bullet on penetrating 30 cm into its target loses its velocity by 50...
Given:
- Initial penetration distance = 30 cm
- Velocity decreases by 50% at this point
To find:
- Additional distance the bullet will penetrate before coming to rest
Assumption:
- The decrease in velocity is directly proportional to the decrease in kinetic energy.
Explanation:
Step 1: Determine the velocity of the bullet when it penetrates 30 cm
- Let the initial velocity of the bullet be V.
- The kinetic energy of the bullet is given by KE = 0.5 * m * V^2, where m is the mass of the bullet.
- When the bullet penetrates 30 cm, its velocity decreases by 50%. So, the final velocity is 0.5V.
- The initial kinetic energy is equal to the final kinetic energy, as there is no external work done on the bullet.
- Therefore, 0.5 * m * V^2 = 0.5 * m * (0.5V)^2.
- Solving this equation, we get V = √(0.5 * 0.25) = 0.5 * √2.
Step 2: Calculate the remaining distance the bullet can penetrate
- The remaining distance the bullet can penetrate is equal to the work done by the bullet.
- The work done is given by W = KE_initial - KE_final.
- Substituting the values, W = 0.5 * m * V^2 - 0.5 * m * (0.5V)^2.
- Simplifying this equation, we get W = 0.5 * m * (V^2 - 0.25V^2).
- W = 0.5 * m * (0.75V^2).
- Since velocity is proportional to the square root of kinetic energy, the remaining distance the bullet can penetrate is proportional to the square root of the remaining kinetic energy.
- Therefore, the remaining distance the bullet can penetrate is equal to √(0.75) times the initial penetration distance of 30 cm.
Step 3: Calculate the additional distance the bullet can penetrate
- The additional distance the bullet can penetrate is given by the difference between the remaining distance and the initial penetration distance.
- Additional distance = √(0.75) * 30 - 30 = 10 cm.
Therefore, the correct answer is option C) 10 cm.
- Initial penetration distance = 30 cm
- Velocity decreases by 50% at this point
To find:
- Additional distance the bullet will penetrate before coming to rest
Assumption:
- The decrease in velocity is directly proportional to the decrease in kinetic energy.
Explanation:
Step 1: Determine the velocity of the bullet when it penetrates 30 cm
- Let the initial velocity of the bullet be V.
- The kinetic energy of the bullet is given by KE = 0.5 * m * V^2, where m is the mass of the bullet.
- When the bullet penetrates 30 cm, its velocity decreases by 50%. So, the final velocity is 0.5V.
- The initial kinetic energy is equal to the final kinetic energy, as there is no external work done on the bullet.
- Therefore, 0.5 * m * V^2 = 0.5 * m * (0.5V)^2.
- Solving this equation, we get V = √(0.5 * 0.25) = 0.5 * √2.
Step 2: Calculate the remaining distance the bullet can penetrate
- The remaining distance the bullet can penetrate is equal to the work done by the bullet.
- The work done is given by W = KE_initial - KE_final.
- Substituting the values, W = 0.5 * m * V^2 - 0.5 * m * (0.5V)^2.
- Simplifying this equation, we get W = 0.5 * m * (V^2 - 0.25V^2).
- W = 0.5 * m * (0.75V^2).
- Since velocity is proportional to the square root of kinetic energy, the remaining distance the bullet can penetrate is proportional to the square root of the remaining kinetic energy.
- Therefore, the remaining distance the bullet can penetrate is equal to √(0.75) times the initial penetration distance of 30 cm.
Step 3: Calculate the additional distance the bullet can penetrate
- The additional distance the bullet can penetrate is given by the difference between the remaining distance and the initial penetration distance.
- Additional distance = √(0.75) * 30 - 30 = 10 cm.
Therefore, the correct answer is option C) 10 cm.
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A bullet on penetrating 30 cm into its target loses its velocity by 50%. What additional distance will it penetrate into the target before it comes to rest?a)30 cmb)20 cmc)10 cmd)5 cmCorrect answer is option 'C'. Can you explain this answer?
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