Question

A projectile has same range for two angles of projection. If times of flight in two cases are t1 and t2 then the range of the projectile is........
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Answer 1

Answer T1 +t2 =2R/g

Explanation

Answer 2

Answer:

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)