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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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