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)

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.