A PROJECTILE HAS SAME RANGE 'R' WHEN MAXIMUM HEIGHT ATTAINED BY IT IS EITHER 'H1' OR 'H2'.FIND THE RELATION BETWEEN,'R','H1','H2'.

Answer 1

The range of a projectile fired at angle A with velocity V is
R = 2(V^2/g)*sinA*cosA
Rmax = (V^2/g) (obtained when A = 45 degrees)
At a given V, you get the same range R when the two angles A1 and A2 are complementary. For example,
R(50 degrees) = R(40 degrees)

Let A1>A2

As for the heights,
H1 = V^2 sin^2A1/(2g)
H2 = V^2 sin^2A2/(2g)
= V^2(cos^2A1)/(2g)

H1^2 + H2^2 = V^4/(4g^2) =
(1/4)*Rmax^2

Where Rmax is the maximum possible range, which is obtained when A = 45 degrees

Answer 2

Correct