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Two boys are standing at the ends A and B of a ground, where AB =a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other boy in a time, T. What is the value of T in terms of a, v and v1?
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Two boys are standing at the ends A and B of a ground, where AB =a. Th...
Let time T and velocity v₁ for boy at B starts running in a perpendicular direction to AB.Given:- boy at A starts running simultaneously with velocity v and time T.Then, by pathagoras theorem_ (v₁T)² + a² = (vT)²(vT)² - (v₁T)² = a² T²( v² - v₁²) =a²T² = a² /(v² - v₁²) T = √{a² /(v² - v₁²)}
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Two boys are standing at the ends A and B of a ground, where AB =a. Th...
Analysis:
To find the value of T in terms of a, v, and v1, we can break down the problem into two components - the horizontal component and the vertical component.
Horizontal Component:
The horizontal component of motion is perpendicular to AB. Since the boy at B starts running in a direction perpendicular to AB, his velocity v1 is entirely in the horizontal direction. Thus, the horizontal distance covered by the boy at B is given by:
Distance = Velocity x Time
D = v1 x T
Vertical Component:
The vertical component of motion is along the line AB. Both boys are running in this direction, but the boy at A is running with a velocity v in the opposite direction. Therefore, the effective velocity of the boy at A is:
Effective Velocity = v + (-v1) = v - v1
The effective velocity is the relative velocity between the two boys. The relative velocity is the difference of their velocities. Since the boy at B is running in the positive direction along AB, his velocity is taken as positive. However, the boy at A is running in the opposite direction, so his velocity is taken as negative.
The effective velocity is used to calculate the time it takes for the boy at A to catch up with the boy at B. The time is given by:
Time = Distance / Effective Velocity
T = a / (v - v1)
Therefore, the value of T in terms of a, v, and v1 is T = a / (v - v1).
To find the value of T in terms of a, v, and v1, we can break down the problem into two components - the horizontal component and the vertical component.
Horizontal Component:
The horizontal component of motion is perpendicular to AB. Since the boy at B starts running in a direction perpendicular to AB, his velocity v1 is entirely in the horizontal direction. Thus, the horizontal distance covered by the boy at B is given by:
Distance = Velocity x Time
D = v1 x T
Vertical Component:
The vertical component of motion is along the line AB. Both boys are running in this direction, but the boy at A is running with a velocity v in the opposite direction. Therefore, the effective velocity of the boy at A is:
Effective Velocity = v + (-v1) = v - v1
The effective velocity is the relative velocity between the two boys. The relative velocity is the difference of their velocities. Since the boy at B is running in the positive direction along AB, his velocity is taken as positive. However, the boy at A is running in the opposite direction, so his velocity is taken as negative.
The effective velocity is used to calculate the time it takes for the boy at A to catch up with the boy at B. The time is given by:
Time = Distance / Effective Velocity
T = a / (v - v1)
Therefore, the value of T in terms of a, v, and v1 is T = a / (v - v1).
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Two boys are standing at the ends A and B of a ground, where AB =a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other boy in a time, T. What is the value of T in terms of a, v and v1?
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Two boys are standing at the ends A and B of a ground, where AB =a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other boy in a time, T. What is the value of T in terms of a, v and v1? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two boys are standing at the ends A and B of a ground, where AB =a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other boy in a time, T. What is the value of T in terms of a, v and v1? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two boys are standing at the ends A and B of a ground, where AB =a. The boy at B starts running in a direction perpendicular to AB with velocity v1. The boy at A starts running simultaneously with velocity v and catches the other boy in a time, T. What is the value of T in terms of a, v and v1?.
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