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A bullet losses 1/n of its velocity in passing through a plank. What is the least no. Of planks required to stop the bullet? (assume constant acceleration)?
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A bullet losses 1/n of its velocity in passing through a plank. What i...
Solution:
Introduction:
When a bullet passes through a plank, it loses 1/n of its velocity. We need to find the minimum number of planks required to stop the bullet.
Concept:
The velocity of the bullet decreases by a factor of 1/n after passing through each plank. We can use the formula for velocity after a certain distance covered with constant retardation, V² - U² = 2as, where V is the final velocity, U is the initial velocity, a is the retardation, and s is the distance covered.
Calculation:
Let the initial velocity of the bullet be U. After passing through the first plank, the velocity becomes U/n. To stop the bullet, the final velocity should be zero. Therefore, the distance covered by the bullet after passing through the first plank is given by:
(U/n)² - U² = -2as
On simplifying, we get:
s = (n² - 1)U²/2an²
The bullet has to pass through n planks. Therefore, the total distance covered by the bullet is:
S = n((n² - 1)U²/2an²)
We need to find the minimum value of n such that S is greater than or equal to the thickness of the planks.
Conclusion:
In conclusion, the minimum number of planks required to stop the bullet is given by:
n = √((U²t)/(2a(U²/n² - U²)))
where t is the thickness of the plank.
Introduction:
When a bullet passes through a plank, it loses 1/n of its velocity. We need to find the minimum number of planks required to stop the bullet.
Concept:
The velocity of the bullet decreases by a factor of 1/n after passing through each plank. We can use the formula for velocity after a certain distance covered with constant retardation, V² - U² = 2as, where V is the final velocity, U is the initial velocity, a is the retardation, and s is the distance covered.
Calculation:
Let the initial velocity of the bullet be U. After passing through the first plank, the velocity becomes U/n. To stop the bullet, the final velocity should be zero. Therefore, the distance covered by the bullet after passing through the first plank is given by:
(U/n)² - U² = -2as
On simplifying, we get:
s = (n² - 1)U²/2an²
The bullet has to pass through n planks. Therefore, the total distance covered by the bullet is:
S = n((n² - 1)U²/2an²)
We need to find the minimum value of n such that S is greater than or equal to the thickness of the planks.
Conclusion:
In conclusion, the minimum number of planks required to stop the bullet is given by:
n = √((U²t)/(2a(U²/n² - U²)))
where t is the thickness of the plank.
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A bullet losses 1/n of its velocity in passing through a plank. What is the least no. Of planks required to stop the bullet? (assume constant acceleration)?
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A bullet losses 1/n of its velocity in passing through a plank. What is the least no. Of planks required to stop the bullet? (assume constant acceleration)? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A bullet losses 1/n of its velocity in passing through a plank. What is the least no. Of planks required to stop the bullet? (assume constant acceleration)? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bullet losses 1/n of its velocity in passing through a plank. What is the least no. Of planks required to stop the bullet? (assume constant acceleration)?.
A bullet losses 1/n of its velocity in passing through a plank. What is the least no. Of planks required to stop the bullet? (assume constant acceleration)? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A bullet losses 1/n of its velocity in passing through a plank. What is the least no. Of planks required to stop the bullet? (assume constant acceleration)? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bullet losses 1/n of its velocity in passing through a plank. What is the least no. Of planks required to stop the bullet? (assume constant acceleration)?.
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