Question

Prove that the maximum horizontal range is four times the maximum height attainedby
the projectile ,when fired at an inclination so as to have maximum horizontal range. (b) If R is the horizontal range for  inclination and h is the maximum height reached by
the projectile ,show that the maximum range is given by (R
2/8h) + 2h

Answer 1

Answer:

$R= gu 2 sin2θ​ ,H= 2gu 2 sin 2 θ​ R max​ = gu 2 ​ forθ=45 0 ,thus,forsameθ,H= 2gu 2 sin 2 45 0 ​ = 4gu 2 ​ HR max​ ​ =4$