A block of mass `m` rests on a wedge of mass `M` which, in trun, rests on a horizontal table, as shown in figure. All surfaces are frictionless. If the system starts at rest with point `P` of the block a distance `h` above the table, find the speed of the wedge the instant point `P` touches the table.

Explanation

As net external force in horizontal direction is zero, `(F_(ext))`horizontal=0
applying momentum conservation conservation in horizontal direction,
`m u_(x)=Mv`………(i)
from constraint we obtain(refere figure-(2)),
`u_(y)=(u_(x)+v)tanalpha`........(ii)
applying conservation of mechanical energy,
`mgh=(1)/(2)m(u_(x)^(2)+u_(y)^(2))+(1)/(2)Mv^(2)`.........(iii)
Solving equation(i),(ii)and(iii),we get
`"v"=sqrt((2mgh)/((M^(2))/(m)+(M)/(2)+(tan^(2)alpha(m+M)^(2))/(m)))`