A body of mass `m` falls from a height `h` and collides with another body of same mass at rest. After collision, the two bodies combine and move through distance `(d)` till they come to rest. Find the work done against the resistive force.

Explanation

Refer to Figure, Here, `m_(1)=m, upsilon_(1)=sqrt(2)gh`
`m_(2)=m, upsilon_(2)=0`
If `upsilon` is the combined velocity after collision, using the principle of conservation of linear momentum,
`m_(1)upsilon_(1)+m_(2)upsilon_(2)=(m_(1)+m_(2))upsilon`
`msqrt(2gh)+0=2m upsilon`
`upsilon=sqrt((gh)/(2))` ...(i)
Work done against resistive forces
`=` energy lost by the combination of bodies
`=(1)/(2)(2m)upsilon^(2)=m(sqrt((gh)/(2)))^(2)=(mgh)/(2)`