One second after projection a stone moves at an angle of 45 degree with the horizontal. Two seconds after projection it moves horizontally .Then what is the angle of projection of the projectile?

Let the angle made by the projectile with the horizontal at a given instant = αLet the angle of projection, velocity of projection be θ, v respectively.Eqn. of x axis x=vtcosθvx=dxdt=vcosθEqn. of y axis y=vtsinθ12gt2vy=dydt=vsinθgtvyvx=vsinθgtvcosθ=tanαat α = 450 t=1=>vsinθgvcosθ=tan450=1=>vsinθg=vcosθ1At t = 2s it moves horizontally so, α=0vsinθ2gvcosθ=tan0=0=>vsinθ2g=0=>vsinθ=2g2.putting eqn. 2 in eqn. 12gg=vcosθ=>vcosθ=g3.Dividing 2 by 3tanθ=2=>θ=tan1(2)

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