Question

Rmax=4Hmax Prooffffff

Answer 1

Time to reach the maximum height H = T = u Sin θ / g


         Range = R = (u Cos θ) * (2 * u sin θ)/g =  u² Sin 2θ / g 

Range is maximum when 2θ = 90⁰  and  Sin 2θ = 1 

           R_max = R = u² / g 

Maximum Height reached = H = u² Sin² θ / 2 g = u² / 4 g = R / 4 


Formula for relation between maximum height and range is : 
            H / R  =  tan θ / 4 

       So H = R / 4           as   tan 45⁰ = 1