A man mass mm takes his date mass mw SolutionInitially Cente

A man (mass mm) takes his date (mass mw

Solution

Initially Center of mass will be

X1 = Mb*x/2 + Mm*x/(Mm + Mb + Mw)

After exchange

X2 = Mb*x/2 + Mw*x/(Mm + Mb + Mw)

Now by momentum conservation

Center of mass will remain same

So

X1 - X2 = d

means boat will move a distance in order to remain same center of mass

d = [Mb*x/2 + Mm*x/(Mm + Mb + Mw)] - [Mb*x/2 + Mw*x/(Mm + Mb + Mw)]

d*(Mm + Mb + Mw) = Mmx - Mw*x

Mw*(x + d) = Mm*x - (Mm + Mb)*d

Mw = Mm*x - (Mm + Mb)*d/(x + d)