Question

In the figure below, a 77 kg man is on a ladder hanging from a balloon that has a total mass of 360 kg (including the basket passenger). The balloon is initially stationary relative to the ground. The man on the ladder begins to climb at 2.5 m/s relative to the ladder. (a) In what direction does the balloon move? upward downward (b) At what speed does the balloon move? m/s (c) If the man then stops climbing, what is the speed of the balloon? m/s

Answer 1

Given is:-

The mass of the man m = 77 kg

Mass of the Balloon M = 360 kg

The speed of the man on the ladder v = 2.5 m/s

Now,

part - a

Let the balloon move up at the speed =  

s { ա Պո —

The man's speed with respect to ground is  

Ug = V – Ub

Now the velocity of the centerr of mass is

Ucm =- mu,+ m(-00) m + m

but

Vam = 0

therefore

un = 90

by plugging all the values we get

(77kg (2.5m/s) 360kg + 77kg

which gives us

Ub = +0.44503m/s

Positive sign here indicates that the balloon is moving upwards.

Part - b

The speed of the balloon is

vp = 0.44503m/s

Part - c

If the man stops climbing then there would be no relative motion within the system because both the man and the balloon are moving with the centerr of mass, which is zero.

Therefore the balloon's speed again becomes zero

up = 0m/s