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The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assume that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:
- a)2.0
- b)1.0
- c)0.5
- d)1.5
Correct answer is option 'C'. Can you explain this answer?
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The velocity of the bullet becomes one third after it penetrates 4 cm ...
Given:
- The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block.
- The bullet stops completely after traveling at (4x) cm inside the block.
To find:
The value of x.
Solution:
Step 1: Understanding the problem
- Let's assume the initial velocity of the bullet is v.
- After penetrating 4 cm in the wooden block, the velocity of the bullet becomes one third, which means its final velocity is v/3.
- The bullet stops completely after traveling (4x) cm inside the block, which means the final velocity is 0.
Step 2: Applying the concept of velocity
- The velocity of an object is given by the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
- In this case, the acceleration is constant and the time taken is not given. So, we need to use another formula to relate the velocities.
Step 3: Using the formula for velocity
- The formula relating initial velocity, final velocity, acceleration, and displacement is v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
- We can use this formula to find the displacement of the bullet inside the wooden block.
Step 4: Calculating the displacement
- The initial velocity of the bullet is v and the final velocity is v/3.
- The displacement is 4 cm.
- Plugging these values into the formula, we get (v/3)^2 = v^2 + 2a(4 cm).
Step 5: Simplifying the equation
- Expanding the equation, we get v^2/9 = v^2 + 8a.
- Multiplying both sides by 9, we get v^2 = 9v^2 + 72a.
- Rearranging the terms, we get 8v^2 = 72a.
- Dividing both sides by 8, we get v^2 = 9a.
Step 6: Using the concept of stopping distance
- The bullet stops completely after traveling (4x) cm inside the block.
- The final velocity is 0.
- Using the formula v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement, we get 0 = v^2 + 2a(4x).
Step 7: Finding the value of x
- Substituting the value of v^2 from the previous equation, we get 0 = 9a + 2a(4x).
- Simplifying the equation, we get 0 = 9a + 8ax.
- Rearranging the terms, we get 8ax = -9a.
- Dividing both sides by a, we get 8x = -9.
- Dividing both sides by 8, we get x = -9/8.
Step 8: Final answer
- The
- The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block.
- The bullet stops completely after traveling at (4x) cm inside the block.
To find:
The value of x.
Solution:
Step 1: Understanding the problem
- Let's assume the initial velocity of the bullet is v.
- After penetrating 4 cm in the wooden block, the velocity of the bullet becomes one third, which means its final velocity is v/3.
- The bullet stops completely after traveling (4x) cm inside the block, which means the final velocity is 0.
Step 2: Applying the concept of velocity
- The velocity of an object is given by the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
- In this case, the acceleration is constant and the time taken is not given. So, we need to use another formula to relate the velocities.
Step 3: Using the formula for velocity
- The formula relating initial velocity, final velocity, acceleration, and displacement is v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
- We can use this formula to find the displacement of the bullet inside the wooden block.
Step 4: Calculating the displacement
- The initial velocity of the bullet is v and the final velocity is v/3.
- The displacement is 4 cm.
- Plugging these values into the formula, we get (v/3)^2 = v^2 + 2a(4 cm).
Step 5: Simplifying the equation
- Expanding the equation, we get v^2/9 = v^2 + 8a.
- Multiplying both sides by 9, we get v^2 = 9v^2 + 72a.
- Rearranging the terms, we get 8v^2 = 72a.
- Dividing both sides by 8, we get v^2 = 9a.
Step 6: Using the concept of stopping distance
- The bullet stops completely after traveling (4x) cm inside the block.
- The final velocity is 0.
- Using the formula v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement, we get 0 = v^2 + 2a(4x).
Step 7: Finding the value of x
- Substituting the value of v^2 from the previous equation, we get 0 = 9a + 2a(4x).
- Simplifying the equation, we get 0 = 9a + 8ax.
- Rearranging the terms, we get 8ax = -9a.
- Dividing both sides by a, we get 8x = -9.
- Dividing both sides by 8, we get x = -9/8.
Step 8: Final answer
- The
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The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assume that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:a)2.0b)1.0c)0.5d)1.5Correct answer is option 'C'. Can you explain this answer?
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The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assume that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:a)2.0b)1.0c)0.5d)1.5Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assume that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:a)2.0b)1.0c)0.5d)1.5Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assume that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is:a)2.0b)1.0c)0.5d)1.5Correct answer is option 'C'. Can you explain this answer?.
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