A man standing at the top of a building, throws several balls at different angles to the horizontal. All balls are thrown at speed u $$=$$ $$10$$ $$m/s$$ and it was found that all of them hit the ground making an angle of $$45$$∘ or larger than that with the horizontal. Find the height of the building (in$$ $$meter). (Take$$ g $$=$$ $$10$$ $$m/s2)

Question

A man standing at the top of a building, throws several balls at different angles to the horizontal. All balls are thrown at speed u $$=$$ $$10$$ $$m/s$$ and it was found that all of them hit the ground making an angle of $$45$$∘ or larger than that with the horizontal. Find the height of the building (in$$ $$meter). (Take$$ g $$=$$ $$10$$ $$m/s2)

Infinity Learn · Accepted Answer

Let h be the height of the building.In $$y-direction$$, $$vy2=uy2+2gh$$            …$$(i)In$$ $$r-direction$$, $$vx=ux$$                       …$$(ii)Also$$, $$tan$$⁡θ$$=vyvxAs$$ per question minimum value of θ is $$45$$∘.⇒Ratio of minimum vy and maximum vx is $$tan$$⁡$$45$$∘$$=1vymin=2gh$$ when y component of initial velocity is minimum, $$uy=0$$ and $$vxmax=u$$ when stone is projected horizontally.∴$$2ghu=1$$⇒$$2$$×$$10h10=1$$, which gives h $$=$$ $$5$$ m.

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