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A ball of mass 50 g is dropped from a he...

A ball of mass 50 g is dropped from a height h = 10 m . It rebounds losing 75 per cent of its kinetic energy . If it remain in contact with the ground for `Deltat = 0.01` s , the impulse of the impact force is

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Balloon is stationary
`rArr` No net external force acts on it.
`rArr` The conservation of linear momentum of the system (ballon + man) is valid
`rArr M vec(v)_(b)+m vec(v)_(m)=0`
where `vec(v)_(m)= vec(v)_(mb)+vec(v)_(b)`
`rArr M vec(v)_(b)+m[vec(v)_(mb)+vec(v)_(b)]=0` where `v_(mb)=` velocity of man relative to the balloon (rope)
`rArr vec(v)_(b)=-(m vec(v)_(mb))/(M+m)`
Where `v_(mb)= v rArr v_(b)=(mv)/(M+m)` and directed opposite to that of the man.
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