Can someone please help me with the first part? Thanks A person weighing 61.3 kg

Question

Can someone please help me with the first part? Thanks

A person weighing 61.3 kg is on a ladder connected to a balloon as shown in the picture. The combined mass of the balloon and the person inside it is 342 kg. Initially the relative velocity of the balloon and the ground is zero. The person on the ladder starts going up with velocity relative to the ladder of 1.29 m/s. Determine the magnitude of the relative velocity between the balloon and the ground. Which way does the balloon move when the person outside starts going up? Select one: Up Down Determine the balloon's speed if the person outside comes to a rest.

Explanation / Answer

Initially the balloon is at rest with respect to ground. So the resultant force on the balloon+men system is zero. So we can apply conservation of momentum pricniple here.

Let the upward direction be positive and downward be negative.

let the velocity of man on ladder with respect to ladder be Vml

let the velocity of man on ladder with respect to ground be Vmg

let the velocity of ladder with respect to ground be Vlg, this will also be the velocity of balloon with respect to ground (Vbg) as ladder is rigidly attatched to the balloon

Now, we have

Vmg = Vml + Vlg -------- (1)

Initially the momentum of the system was zero. And then the man on ladder starts with velocity Vml = +1.29m/s

Now applying momentum conservation principle we have;

0 = (61.3kg)Vmg + (342kg)Vlg (since the balloon is connected to ladder the mass associated with ladder's velocity would be 342kg)

or (61.3kg)Vmg + (342kg)(Vmg - Vml) = 0

or Vmg(61.3kg + 342kg) = (342kg)Vml

or Vmg(403.3kg) = (342kg)(1.29m/s)

or Vmg = 1.093m/s, puttin this value in equation (1) we get

Vmg = Vml + Vlg

1.093m/s = 1.29m/s +  Vlg

or  Vlg = -0.196m/s

So the velocity of ladder with respect to ground is Vlg = -0.196m/s, negative direction shows that the ladder is going down with respect to ground, as we took the upward direction to be positive and downward to be negative.

Since the ladder and balloon are connected, the  velocity of ladder with respect to ground =  velocity of balloon with respect to ground,

Thus magnitude of relative velocity between the balloon and the ground is 0.196m/s

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This concludes the answers. Check the answer and let me know if it's correct. If you need anymore clarification or correction I will be happy to oblige....

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