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A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s?
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A horizontal board is being moved with a constant velocity v =20m\s on...
Given parameters:
- Velocity of the board (v) = 20 m/s
- Velocity of the block (u) = 25 m/s
- Angle of projection relative to ground (θ) = 37 degrees
- Coefficient of friction between block and board (μ) = 0.3
- Time elapsed (t) = 10 seconds
Calculating the horizontal and vertical components of velocity:
- The horizontal component of velocity (u cosθ) = 25 cos37° = 19.97 m/s
- The vertical component of velocity (u sinθ) = 25 sin37° = 15.07 m/s
Calculating the initial velocity of the block relative to the board:
- The initial velocity of the block relative to the board in the horizontal direction = 19.97 - 20 = -0.03 m/s
- The initial velocity of the block relative to the board in the vertical direction = 15.07 m/s
Calculating the acceleration of the block relative to the board:
- The gravitational force acting on the block (mg) = 0.1 kg * 9.81 m/s^2 = 0.981 N
- The force of friction (f) = μ * m * g = 0.3 * 0.1 kg * 9.81 m/s^2 = 0.2943 N
- The net force (F) = ma (where m is the mass of the block)
- F = m * a = m * (g - f) = 0.1 kg * (9.81 - 0.2943) m/s^2 = 0.95657 N
- The acceleration of the block = F / m = 0.95657 / 0.1 = 9.5657 m/s^2
Calculating the final velocity of the block relative to the board:
- The final velocity of the block relative to the board in the horizontal direction = -0.03 m/s + (0 m/s^2 * 10 s) = -0.03 m/s
- The final velocity of the block relative to the board in the vertical direction = 15.07 m/s + (9.5657 m/s^2 * 10 s) = 110.727 m/s
Calculating the velocity of the block relative to the ground:
- The velocity of the block relative to the ground in the horizontal direction = -0.03 m/s + 20 m/s = 19.97 m/s
- The velocity of the block relative to the ground in the vertical direction = 110.727 m/s
Answer:
The velocity of the block relative to the ground after 10 seconds is approximately 111 m/s in the vertical direction and 20 m/s in the horizontal direction.
- Velocity of the board (v) = 20 m/s
- Velocity of the block (u) = 25 m/s
- Angle of projection relative to ground (θ) = 37 degrees
- Coefficient of friction between block and board (μ) = 0.3
- Time elapsed (t) = 10 seconds
Calculating the horizontal and vertical components of velocity:
- The horizontal component of velocity (u cosθ) = 25 cos37° = 19.97 m/s
- The vertical component of velocity (u sinθ) = 25 sin37° = 15.07 m/s
Calculating the initial velocity of the block relative to the board:
- The initial velocity of the block relative to the board in the horizontal direction = 19.97 - 20 = -0.03 m/s
- The initial velocity of the block relative to the board in the vertical direction = 15.07 m/s
Calculating the acceleration of the block relative to the board:
- The gravitational force acting on the block (mg) = 0.1 kg * 9.81 m/s^2 = 0.981 N
- The force of friction (f) = μ * m * g = 0.3 * 0.1 kg * 9.81 m/s^2 = 0.2943 N
- The net force (F) = ma (where m is the mass of the block)
- F = m * a = m * (g - f) = 0.1 kg * (9.81 - 0.2943) m/s^2 = 0.95657 N
- The acceleration of the block = F / m = 0.95657 / 0.1 = 9.5657 m/s^2
Calculating the final velocity of the block relative to the board:
- The final velocity of the block relative to the board in the horizontal direction = -0.03 m/s + (0 m/s^2 * 10 s) = -0.03 m/s
- The final velocity of the block relative to the board in the vertical direction = 15.07 m/s + (9.5657 m/s^2 * 10 s) = 110.727 m/s
Calculating the velocity of the block relative to the ground:
- The velocity of the block relative to the ground in the horizontal direction = -0.03 m/s + 20 m/s = 19.97 m/s
- The velocity of the block relative to the ground in the vertical direction = 110.727 m/s
Answer:
The velocity of the block relative to the ground after 10 seconds is approximately 111 m/s in the vertical direction and 20 m/s in the horizontal direction.
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A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s?
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A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s?.
A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s?.
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A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s?, a detailed solution for A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s? has been provided alongside types of A horizontal board is being moved with a constant velocity v =20m\s on a smooth horizontal plane.a small block is projected on the block with velocity v=25m\s at an angle of 37 degrees relative to the ground.the coefficient of friction between the block and the board is 0.3.find the velocity of block relative to ground after t=10s? theory, EduRev gives you an
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