Prove that the maximum horizontal range is 4 times the max height attained by the projectile fired at an inclination - Physics - Motion In A Plane

Question

Prove that the maximum horizontal range is 4 times the max
height attained by the projectile fired at an inclination so as to
have maximum horizontal range

123456789 · Accepted Answer

For maximum horizontal range, angle of inclination x = 45
degrees
Hence when x = 45,
Maximum range = u2Sin2x / g
= u2 Sin2(45) / g = u2 (1) * (1/g)=
u2 /g
Maximum Height =u2Sin2x / 2g
=u2Sin2(45) / 2g =u2 (1/2) *
(1/2g) =u2/ 4g
Hence Maximum range
(u2/g)is 4 times the Maximum
height (u2/
4g)when it attains maximum horizontal
range

Prove that the maximum horizontal range is 4 times the max height attained by the projectile fired at an inclination so as to have maximum horizontal range