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A man of mass 50 kg mass is standing in a gravity free space at a height of 10m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2m/sec. When the stone reaches the floor, the distance of the man above the floor
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A man of mass 50 kg mass is standing in a gravity free space at a heig...
Problem: A man throws a stone downwards while standing in a gravity-free space. Find his distance from the floor when the stone reaches the ground.
Given:
- Mass of man (mm) = 50 kg
- Mass of stone (ms) = 0.5 kg
- Height of man from the floor (h) = 10 m
- Initial velocity of stone (u) = 2 m/s
Calculations:
- Initial momentum of man-stone system = mmum + msus
- Final momentum of man-stone system = mmvm + msvs (where vm is the final velocity of the man and vs is the final velocity of the stone)
- Since there is no external force acting on the man-stone system, momentum is conserved. Therefore, initial momentum = final momentum.
- Using the conservation of momentum equation, we get: mmum + msus = mmvm + msvs
- As the man is in a gravity-free space, there is no external force acting on him. Therefore, his velocity remains constant at zero. Hence, vm = 0.
- When the stone reaches the ground, its final velocity (vs) can be calculated using the equation of motion: vs2 = us2 + 2gh (where g is acceleration due to gravity and h is the height of the man from the floor)
- Substituting the given values, we get: vs2 = 4 + 2(9.8)(10) = 204.4
- Therefore, vs = sqrt(204.4) = 14.28 m/s
- Using the conservation of momentum equation, we get: 50(0) + 0.5(2) = 50vm + 0.5(14.28)
- Solving for vm, we get: vm = 0.014 m/s
- Now, using the equation of motion: h = ut + (1/2)gt2 (where t is the time taken by the stone to reach the ground)
- Substituting the given values, we get: 10 = 0 + (1/2)(9.8
Community Answer
A man of mass 50 kg mass is standing in a gravity free space at a heig...
10.1 m
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A man of mass 50 kg mass is standing in a gravity free space at a height of 10m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2m/sec. When the stone reaches the floor, the distance of the man above the floor
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A man of mass 50 kg mass is standing in a gravity free space at a height of 10m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2m/sec. When the stone reaches the floor, the distance of the man above the floor for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A man of mass 50 kg mass is standing in a gravity free space at a height of 10m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2m/sec. When the stone reaches the floor, the distance of the man above the floor covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man of mass 50 kg mass is standing in a gravity free space at a height of 10m above the floor. He throws a stone of 0.5 kg mass downwards with a speed 2m/sec. When the stone reaches the floor, the distance of the man above the floor.
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