Question

a ballon of massM is stationary in air it has a ladder on which a man of mass m is standing .i f the man starts climbing up the ladder with velocityv relative to ladder, yhe the velo ity of ballon is​

Answer 1

Answer:

The momentum of this system consisting of both the balloon and the man will remain constant in the vertical direction.

So, if the man starts climbing up with velocity v relative to the ladder, however ladder connected to the balloon will itself actually start coming down with some velocity let us suppose v' which we want to find.

Now,

vectorally

velocity of man wrt ladder = Velocity of man - Velocity of ladder

v = u - (-v')

-v' because of balloon will be downwards and hence considering it as negative however considering man ladder Velocity as positive.

So,

u = v-v'

Now,

by momentum conservation

0 = m(v-v') - Mv'

so,

v' = mv/m+M

Hope this helps you !