Question

A balloon of mass M is floating motionless in the air. A person of mass less than M is on a rope ladder hanging from the balloon. The person begins to climb the ladder at a uniform speed v relative to the ground. How does the balloon move relative to the ground?

Answer 1

Answer:

Down with a speed less than v

Explanation:

Let the person's mass be represented by m

The mass of the balloon = M

Total momentum is conserved thus F = external force = 0

when the person starts to climb the ladder, external force is still equal to zero.

We know that change is p = F * change in t

in this equation, F is the external force = 0

Hence change in p = 0

This means that total momentum is conserved thus F = external force = 0

(owing to the fact that exterior forces on the system are balanced)

Since all external force was zero before they began to climb the ladder, as they climb all external forces will still = 0

Thus, As the person starts moving

mv + MV = 0

or mv = MV

V = mv/M

Since M > m, m/M will definitely be a number that is less than 1,

Hence, V = (a number less than 1)v.

This means that V < v, or the balloon moves down a speed V which is less than v.