A bomber plane moving at a horizontal speed of $$20$$ $$m/s$$ releases a bomb at a height of $$80$$ m above ground as shown in figure. At the same instant, a hunter of negligible height starts running from a point below it, to catch the bomb with speed $$10$$ $$m/s$$. After $$2s$$, he realised that he cannot make it, he stops running and immediately holds his gun and fires in such direction so that just before bomb hits the ground, bullet will hit it. What should be the firing speed of bullet? (Take$$, g $$=$$ $$10$$ $$m/s2)

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Infinity Learn · Accepted Answer

$$T=2Hg=2(80)10=4sR=uT=20$$×$$4=80mIn$$ $$2$$ s, hunter will travel $$10$$×$$2=20mFor$$ bullet, $$T=2usin$$⁡θ$$g=4$$−$$2=2s$$ …….(i) $$2usin$$⁡θ$$g=2s$$⇒usin⁡θ$$=10---(1)$$                   $$R=u2sin$$⁡$$2$$θ$$g=80$$−$$20=60m$$  ……..(ii)From$$ Eqs. $$(i) and (ii), we $$getu22sin$$⁡θ$$cos$$θgusinθ$$=6010tan$$⁡θ$$=13$$ and $$u=1010m/s$$

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