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A bullet is fired aiming target as shown...

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.

Text Solution

Verified by Experts

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.
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