A bullet is fired aiming target as shown. If the target is dropped from rest at the same time then prove that it will hit to target.

Explanation

from
`AB=h=x tan theta`
Let bullet collide to target after time t
`{:("then y-coordinate of target",,y_(T)=x tan theta -1/2 g t^(2)...(1)),("and y-coordinate of bullet",,y_(b)=u sin theta xt-1/2 g t^(2)...(2)),("But if",,y_(T)=y_(b)),("then",,x tan theta-1/2g t^(2)=u sin theta xt-1/2 g t^(2)...(3)),("x-coordinate of bullet",,x_(b)=x=ucos thetat),(,,t=x/(u cos theta)" ""placeing in equation (3)"),(,,x tan theta -1/2 g t^(2)=x tan theta-1/2 g t^(2)):}` L.H.S.=R.H.S.
So bullet ccollide with target.