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A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time?
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A small block can move in a straight horizontal line along AB. Flash l...
Analysis of the problem:
The block moving along AB will project its shadow on the vertical wall in the shape of a circle due to the circular cross-section of the wall. The radial acceleration of the shadow can be found by analyzing the motion of the block.
Derivation of radial acceleration:
- The block moves horizontally along AB with a certain velocity v.
- The shadow of the block on the wall moves in a circular path with a radius equal to the distance between AB and the wall.
- The radial acceleration of the shadow can be calculated using the formula for centripetal acceleration: ar = v^2 / r, where v is the velocity of the block and r is the radius of the circular path.
Expressing radial acceleration as a function of time:
- The velocity of the block can be expressed as v = dx / dt, where dx is the displacement of the block along AB and dt is the change in time.
- The radius of the circular path can be expressed as r = √(x^2 + h^2), where x is the horizontal distance of the block from the wall and h is the height of the wall.
- Substituting the expressions for velocity and radius into the formula for radial acceleration, we get ar = (dx / dt)^2 / √(x^2 + h^2).
Conclusion:
The radial acceleration of the shadow on the vertical wall, as a function of time, can be expressed as ar = (dx / dt)^2 / √(x^2 + h^2). This analysis provides an understanding of the relationship between the motion of the block along AB and the radial acceleration of its shadow on the wall.
The block moving along AB will project its shadow on the vertical wall in the shape of a circle due to the circular cross-section of the wall. The radial acceleration of the shadow can be found by analyzing the motion of the block.
Derivation of radial acceleration:
- The block moves horizontally along AB with a certain velocity v.
- The shadow of the block on the wall moves in a circular path with a radius equal to the distance between AB and the wall.
- The radial acceleration of the shadow can be calculated using the formula for centripetal acceleration: ar = v^2 / r, where v is the velocity of the block and r is the radius of the circular path.
Expressing radial acceleration as a function of time:
- The velocity of the block can be expressed as v = dx / dt, where dx is the displacement of the block along AB and dt is the change in time.
- The radius of the circular path can be expressed as r = √(x^2 + h^2), where x is the horizontal distance of the block from the wall and h is the height of the wall.
- Substituting the expressions for velocity and radius into the formula for radial acceleration, we get ar = (dx / dt)^2 / √(x^2 + h^2).
Conclusion:
The radial acceleration of the shadow on the vertical wall, as a function of time, can be expressed as ar = (dx / dt)^2 / √(x^2 + h^2). This analysis provides an understanding of the relationship between the motion of the block along AB and the radial acceleration of its shadow on the wall.
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A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time?
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A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time?.
A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A small block can move in a straight horizontal line along AB. Flash lights from one side project its shadow on a vertical wall which has a horizontal cross-section as a circle. Find radial acceleration as a function of time?.
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