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A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m per second in same Direction What is their common velocity?
Most Upvoted Answer
A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 k...
This question is based on conservation of momentum...
initial momentum= final momentum..
common velocity means both trolley and boy moves with same velocity..
initial momentum=60×3+140×1.5
=180 + 210
=390 kgm/s
final momentum=(60+140)V
200V
so on equating..
200V=390
V=390/200=1.95m/s...
initial momentum= final momentum..
common velocity means both trolley and boy moves with same velocity..
initial momentum=60×3+140×1.5
=180 + 210
=390 kgm/s
final momentum=(60+140)V
200V
so on equating..
200V=390
V=390/200=1.95m/s...
Community Answer
A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 k...
Solution:
To find the common velocity of the boy and trolley, we need to apply the law of conservation of momentum.
Law of conservation of momentum
- In an isolated system, the total momentum before the interaction is equal to the total momentum after the interaction.
- In other words, the sum of the initial momenta of the objects is equal to the sum of the final momenta of the objects.
- Mathematically, we can express this as:
m1v1i + m2v2i = m1v1f + m2v2f
- where m1 and m2 are the masses of the objects, v1i and v2i are their initial velocities, and v1f and v2f are their final velocities.
Applying the law of conservation of momentum
Let's apply the law of conservation of momentum to the given situation.
- Initial momentum of the boy = mboyvboyi = 60 kg x 3 m/s = 180 kg m/s
- Initial momentum of the trolley = mtrolleyvtrolleyi = 140 kg x 1.5 m/s = 210 kg m/s
- Total initial momentum = 180 kg m/s + 210 kg m/s = 390 kg m/s
- Let's assume the common velocity of the boy and the trolley after the interaction is vcommon.
- Final momentum of the boy = mboyvcommon
- Final momentum of the trolley = mtrolleyvcommon
- Total final momentum = mboyvcommon + mtrolleyvcommon = (mboy + mtrolley)vcommon
- According to the law of conservation of momentum, total initial momentum = total final momentum.
390 kg m/s = (60 kg + 140 kg) vcommon
Solving for vcommon, we get:
vcommon
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A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m per second in same Direction What is their common velocity?
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A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m per second in same Direction What is their common velocity? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m per second in same Direction What is their common velocity? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m per second in same Direction What is their common velocity?.
A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m per second in same Direction What is their common velocity? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m per second in same Direction What is their common velocity? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A boy of mass 60kg running at 3ms1 jumps on to a trolley of mass 140 kg moving with a velocity of 1.5 m per second in same Direction What is their common velocity?.
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