Question

prove that the horizontal range of a projectile is same for two angles of projection

Answer 1

A Projectile has Same range for 2 diff. angles  R1=R2

THIS IMPLIES THAT

Angle of projectile 1 +Angle of Projectile 2 =90(Simple rule Can be proved if required)

Let                  a      +              b              =90

a=90-b

sin a =cos b

T1 = 2 u sin a/g ;;  T1 =2 u cos b/g ; ;cos b=T1 .g /2u

T2= 2 u sin b/g ;;  sin b=T2.g/2u

R2 = u*u*sin2b/g

=u*u*2sin b cos b/g

SUBSTITUTE THE VALUES

=u*u*2*T2.g.T1.g/g.2u.2u

=T2*T1*g/2

(WE HAVE ASSUMED THAT THE PROJECTILES HAVE SAME INITIAL VELOCITY

AND ARE PROJECTED FROM SAME POINTS SIMULTANEOUSLY)