Question

Prove that the maximum horizontal range is four times the maximum height attained by the projectile, when fired at an inclination so as to have maximum horizontal range.

Answer 1

For maximum range angle of projection is 45°.

Rmax = u²sin2 theta/g

= u²sin 2*45/g

= u²sin90/g

= u²/g

Now,

Hmax = u²sin² theta/2g

= u²sin²45/2g

= u²/4g

Therefore, horizontal range is 4 times the maximum height, hence proved.