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Two balls are thrown simultaneously from the same point horizontally in same opposite direction with velocities V1 equal to 3 metre per second and V2 equal to 4 metre per second find the distance between them that moment when the velocity seem to be mutually perpendicular?
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Two balls are thrown simultaneously from the same point horizontally i...
Explanation:
When two balls are thrown horizontally in opposite directions, their vertical components of velocity are zero. Therefore, the only relative motion between the balls is in the horizontal direction. Let's assume that the distance between the balls at the time when their velocities are perpendicular is d.
Calculating the time:
To calculate the time at which the velocities of the balls are perpendicular, we need to use the concept of relative velocity. The relative velocity of ball 1 with respect to ball 2 is (V1 + V2), as both balls are moving in opposite directions. Therefore, the time taken for the balls to reach the point where their velocities are perpendicular is given by the formula:
t = d / (V1 + V2)
Calculating the distance:
To find the distance between the balls at this moment, we need to calculate the distance covered by each ball in this time. The distance covered by ball 1 is given by:
d1 = V1 * t = V1 * d / (V1 + V2)
Similarly, the distance covered by ball 2 is given by:
d2 = V2 * t = V2 * d / (V1 + V2)
Therefore, the distance between the balls when their velocities are perpendicular is given by:
d = d1 + d2 = V1 * d / (V1 + V2) + V2 * d / (V1 + V2)
Simplifying this equation, we get:
d = (V1 * V2 * t) / (V1 + V2)
Substituting the value of t in terms of d, we get:
d = (V1 * V2 * d) / [(V1 + V2)^2]
Simplifying this equation, we get:
d = (V1 * V2) / (V1 + V2)
Therefore, the distance between the balls when their velocities are perpendicular is:
d = (V1 * V2) / (V1 + V2) = (3 * 4) / (3 + 4) = 12 / 7 meters
Conclusion:
Hence, the distance between the balls at the moment when their velocities are perpendicular is 12/7 meters.
When two balls are thrown horizontally in opposite directions, their vertical components of velocity are zero. Therefore, the only relative motion between the balls is in the horizontal direction. Let's assume that the distance between the balls at the time when their velocities are perpendicular is d.
Calculating the time:
To calculate the time at which the velocities of the balls are perpendicular, we need to use the concept of relative velocity. The relative velocity of ball 1 with respect to ball 2 is (V1 + V2), as both balls are moving in opposite directions. Therefore, the time taken for the balls to reach the point where their velocities are perpendicular is given by the formula:
t = d / (V1 + V2)
Calculating the distance:
To find the distance between the balls at this moment, we need to calculate the distance covered by each ball in this time. The distance covered by ball 1 is given by:
d1 = V1 * t = V1 * d / (V1 + V2)
Similarly, the distance covered by ball 2 is given by:
d2 = V2 * t = V2 * d / (V1 + V2)
Therefore, the distance between the balls when their velocities are perpendicular is given by:
d = d1 + d2 = V1 * d / (V1 + V2) + V2 * d / (V1 + V2)
Simplifying this equation, we get:
d = (V1 * V2 * t) / (V1 + V2)
Substituting the value of t in terms of d, we get:
d = (V1 * V2 * d) / [(V1 + V2)^2]
Simplifying this equation, we get:
d = (V1 * V2) / (V1 + V2)
Therefore, the distance between the balls when their velocities are perpendicular is:
d = (V1 * V2) / (V1 + V2) = (3 * 4) / (3 + 4) = 12 / 7 meters
Conclusion:
Hence, the distance between the balls at the moment when their velocities are perpendicular is 12/7 meters.
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Two balls are thrown simultaneously from the same point horizontally in same opposite direction with velocities V1 equal to 3 metre per second and V2 equal to 4 metre per second find the distance between them that moment when the velocity seem to be mutually perpendicular?
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Two balls are thrown simultaneously from the same point horizontally in same opposite direction with velocities V1 equal to 3 metre per second and V2 equal to 4 metre per second find the distance between them that moment when the velocity seem to be mutually perpendicular? 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 Two balls are thrown simultaneously from the same point horizontally in same opposite direction with velocities V1 equal to 3 metre per second and V2 equal to 4 metre per second find the distance between them that moment when the velocity seem to be mutually perpendicular? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two balls are thrown simultaneously from the same point horizontally in same opposite direction with velocities V1 equal to 3 metre per second and V2 equal to 4 metre per second find the distance between them that moment when the velocity seem to be mutually perpendicular?.
Two balls are thrown simultaneously from the same point horizontally in same opposite direction with velocities V1 equal to 3 metre per second and V2 equal to 4 metre per second find the distance between them that moment when the velocity seem to be mutually perpendicular? 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 Two balls are thrown simultaneously from the same point horizontally in same opposite direction with velocities V1 equal to 3 metre per second and V2 equal to 4 metre per second find the distance between them that moment when the velocity seem to be mutually perpendicular? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two balls are thrown simultaneously from the same point horizontally in same opposite direction with velocities V1 equal to 3 metre per second and V2 equal to 4 metre per second find the distance between them that moment when the velocity seem to be mutually perpendicular?.
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