Two particles are projected upwards with the same initial velocity v0 in two different angles of projection such that their horizontal ranges are the same. The ratio of the heights of their highest point will be

As the horizontal ranges are the same.∴  v02sin2θ1g=v02sin2θ2gSo,  sin2θ1 = sin2θ2or         2θ1 = π - 2θ2⇒   θ1 + θ2 = π/2∴  h1max=v02sin2θ12gand  h2max=v02sin2θ22g∴  h1maxh2max=sin2θ1sin2θ2=sin2θ1cos2θ1=tan2θ1                                   ∵sin2θ2=sin2π2-θ1=cos2θ1