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Two billiard balls are moving on a table and the component velocities along the length and breadth are 5,5m/s for one ball2 root3,2m/s for the other ball the angle between the motion of balls is 1)30 degrees 2)60 degrees 3)40 degrees 4)15 degrees Pls solve this question?
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Two billiard balls are moving on a table and the component velocities ...
Given information:
- Velocity of ball 1 along length = 5 m/s
- Velocity of ball 1 along breadth = 5 m/s
- Velocity of ball 2 along length = 2√3 m/s
- Velocity of ball 2 along breadth = 2 m/s
Calculating the angle between the motions of the balls:
- Let the angle between the motions of the balls be θ.
- The dot product of the velocities of the two balls gives:
V1 • V2 = |V1||V2|cosθ
- Substituting the given values:
(5*2√3) + (5*2) = 5*2√3*2*cosθ
10√3 + 10 = 20√3*cosθ
10(√3 + 1) = 20√3*cosθ
(√3 + 1) = 2√3*cosθ
cosθ = (√3 + 1) / 2√3
Solving for the angle:
1) For θ = 30 degrees:
- cos30 = √3/2
- (√3 + 1) / 2√3 ≠ √3/2
- Hence, θ ≠ 30 degrees
2) For θ = 60 degrees:
- cos60 = 1/2
- (√3 + 1) / 2√3 = 1/2
- Hence, θ = 60 degrees
Therefore, the angle between the motions of the balls is 60 degrees.
- Velocity of ball 1 along length = 5 m/s
- Velocity of ball 1 along breadth = 5 m/s
- Velocity of ball 2 along length = 2√3 m/s
- Velocity of ball 2 along breadth = 2 m/s
Calculating the angle between the motions of the balls:
- Let the angle between the motions of the balls be θ.
- The dot product of the velocities of the two balls gives:
V1 • V2 = |V1||V2|cosθ
- Substituting the given values:
(5*2√3) + (5*2) = 5*2√3*2*cosθ
10√3 + 10 = 20√3*cosθ
10(√3 + 1) = 20√3*cosθ
(√3 + 1) = 2√3*cosθ
cosθ = (√3 + 1) / 2√3
Solving for the angle:
1) For θ = 30 degrees:
- cos30 = √3/2
- (√3 + 1) / 2√3 ≠ √3/2
- Hence, θ ≠ 30 degrees
2) For θ = 60 degrees:
- cos60 = 1/2
- (√3 + 1) / 2√3 = 1/2
- Hence, θ = 60 degrees
Therefore, the angle between the motions of the balls is 60 degrees.
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Two billiard balls are moving on a table and the component velocities along the length and breadth are 5,5m/s for one ball2 root3,2m/s for the other ball the angle between the motion of balls is 1)30 degrees 2)60 degrees 3)40 degrees 4)15 degrees Pls solve this question?
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Two billiard balls are moving on a table and the component velocities along the length and breadth are 5,5m/s for one ball2 root3,2m/s for the other ball the angle between the motion of balls is 1)30 degrees 2)60 degrees 3)40 degrees 4)15 degrees Pls solve this question? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two billiard balls are moving on a table and the component velocities along the length and breadth are 5,5m/s for one ball2 root3,2m/s for the other ball the angle between the motion of balls is 1)30 degrees 2)60 degrees 3)40 degrees 4)15 degrees Pls solve this question? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two billiard balls are moving on a table and the component velocities along the length and breadth are 5,5m/s for one ball2 root3,2m/s for the other ball the angle between the motion of balls is 1)30 degrees 2)60 degrees 3)40 degrees 4)15 degrees Pls solve this question?.
Two billiard balls are moving on a table and the component velocities along the length and breadth are 5,5m/s for one ball2 root3,2m/s for the other ball the angle between the motion of balls is 1)30 degrees 2)60 degrees 3)40 degrees 4)15 degrees Pls solve this question? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Two billiard balls are moving on a table and the component velocities along the length and breadth are 5,5m/s for one ball2 root3,2m/s for the other ball the angle between the motion of balls is 1)30 degrees 2)60 degrees 3)40 degrees 4)15 degrees Pls solve this question? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two billiard balls are moving on a table and the component velocities along the length and breadth are 5,5m/s for one ball2 root3,2m/s for the other ball the angle between the motion of balls is 1)30 degrees 2)60 degrees 3)40 degrees 4)15 degrees Pls solve this question?.
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