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Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.?
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Q13) A piece of wood of mass 0.03kg is dropped from the top of a build...
Introduction
To solve this problem, we will analyze the motion of both the wooden piece and the bullet until they collide and then determine the maximum height they achieve together.
Step 1: Calculate the time taken for the wooden piece to fall
- The wooden piece is dropped from a height of 100m.
- Using the equation of motion: h = 0.5 * g * t^2, where g = 9.8 m/s².
- Rearranging gives: t = sqrt(2h/g) = sqrt(2 * 100 / 9.8) ≈ 4.52 seconds.
Step 2: Calculate the height reached by the bullet
- The bullet is fired upwards with an initial velocity of 100 m/s.
- The time taken for the bullet to reach its maximum height (where final velocity is 0): t = u/g = 100/9.8 ≈ 10.2 seconds.
- The bullet will reach a height: h = ut - 0.5 * g * t^2 = 100 * 10.2 - 0.5 * 9.8 * (10.2)^2 = 510m (but it will only travel for 4.52 seconds before meeting the wooden piece).
Step 3: Calculate the height of the bullet at t = 4.52 seconds
- Height = u * t - 0.5 * g * t^2 = 100 * 4.52 - 0.5 * 9.8 * (4.52)^2 ≈ 202.6m.
Step 4: Determine the height of the collision
- The wooden piece falls 100m down to ground level, while the bullet rises approximately 202.6m.
- The collision occurs at a height of 100m - (100 - 202.6) = 202.6m from the ground.
Step 5: Conservation of Momentum
- Before collision: Momentum = (0.03 * 0) + (0.02 * 100) = 2 kg·m/s.
- After collision, let v be the velocity of the combined mass (0.03kg + 0.02kg = 0.05kg).
- Therefore, 2 = 0.05v implying v = 40 m/s.
Step 6: Maximum height after collision
- Use the equation: v^2 = u^2 - 2gh, where u = 40 m/s.
- Setting the final velocity (v) to 0 at maximum height:
0 = 40^2 - 2 * 9.8 * h.
- Solving gives h ≈ 81.63 m.
Step 7: Total height above the building
- Finally, adding the height of the building: Total height = 100m + 81.63m = 181.63m.
Conclusion
The combination of the wooden piece and the bullet rises to a height of approximately 181.63 meters above the ground before starting to fall back down.
To solve this problem, we will analyze the motion of both the wooden piece and the bullet until they collide and then determine the maximum height they achieve together.
Step 1: Calculate the time taken for the wooden piece to fall
- The wooden piece is dropped from a height of 100m.
- Using the equation of motion: h = 0.5 * g * t^2, where g = 9.8 m/s².
- Rearranging gives: t = sqrt(2h/g) = sqrt(2 * 100 / 9.8) ≈ 4.52 seconds.
Step 2: Calculate the height reached by the bullet
- The bullet is fired upwards with an initial velocity of 100 m/s.
- The time taken for the bullet to reach its maximum height (where final velocity is 0): t = u/g = 100/9.8 ≈ 10.2 seconds.
- The bullet will reach a height: h = ut - 0.5 * g * t^2 = 100 * 10.2 - 0.5 * 9.8 * (10.2)^2 = 510m (but it will only travel for 4.52 seconds before meeting the wooden piece).
Step 3: Calculate the height of the bullet at t = 4.52 seconds
- Height = u * t - 0.5 * g * t^2 = 100 * 4.52 - 0.5 * 9.8 * (4.52)^2 ≈ 202.6m.
Step 4: Determine the height of the collision
- The wooden piece falls 100m down to ground level, while the bullet rises approximately 202.6m.
- The collision occurs at a height of 100m - (100 - 202.6) = 202.6m from the ground.
Step 5: Conservation of Momentum
- Before collision: Momentum = (0.03 * 0) + (0.02 * 100) = 2 kg·m/s.
- After collision, let v be the velocity of the combined mass (0.03kg + 0.02kg = 0.05kg).
- Therefore, 2 = 0.05v implying v = 40 m/s.
Step 6: Maximum height after collision
- Use the equation: v^2 = u^2 - 2gh, where u = 40 m/s.
- Setting the final velocity (v) to 0 at maximum height:
0 = 40^2 - 2 * 9.8 * h.
- Solving gives h ≈ 81.63 m.
Step 7: Total height above the building
- Finally, adding the height of the building: Total height = 100m + 81.63m = 181.63m.
Conclusion
The combination of the wooden piece and the bullet rises to a height of approximately 181.63 meters above the ground before starting to fall back down.
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Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.?
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Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.?.
Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.?.
Solutions for Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.? in English & in Hindi are available as part of our courses for UPSC.
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Here you can find the meaning of Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.? defined & explained in the simplest way possible. Besides giving the explanation of
Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.?, a detailed solution for Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.? has been provided alongside types of Q13) A piece of wood of mass 0.03kg is dropped from the top of a building 100m high. At the same time, a bullet of mass 0.02kg is fired vertically upwards with a velocity of 100m/s from the ground. The bullet gets embedded in the wooden piece after striking. Find the height (in m) above the building to which the combination rises, before it starts falling down. Air friction is zero. When they meet and stick together, assume no effect of gravity in that very tiny duration.? theory, EduRev gives you an
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