Question

On a horizontal frictional frozon lake , a girl(36 kg) and box (9kg) are connected to each other by means of a rope. Initally they are 20 m apart . The girl exerts a horizontal force on the box ,pulling it towards her . How far has the girl travelled when she meet the box ?

Answer 1

The girl and box moves towards each other by keeping conservation of momentum principle.
When the box recahes the girl , both of them become rest. so momentum will be zero at final stage , so by law conservation of momentum principle, total momentum of girl and box at initial stage will be equal to zero.

Let MV be momentum of girl and mv be momentum of the box.

MV+mv=0
MV= - mv
negative sign implies they will be movig in opposite direction.

so 36 x V = 9 x v
so v = 4V
box will have velocity four times than girl.

Also they are in opposite direction,
relative velocity = v + V = 5V

time taken to meet = distance between them / relative evelocity
= 20 / 5V = 4/V

if V=1 , t=4 s
if V= 2 , t=2 s
if V=3 , t =4/3 s

The answer will be based on the velocity of girl moving .

As velocity is not given in te question, answer will written in the variable of velocity

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