Question

A projectile can have the same range R for two angles of projection. T1 and T2 be the time of flight in the two cases, then the initial velocity of the projectile is?

Answer 1

t1=2vsinθgt1=2vsin⁡θgt2=2vsin(90∘−θ)g=2vcosθgt2=2vsin⁡(90∘−θ)g=2vcos⁡θgNow,t1t2=(2vsinθ)(2vcosθ)g2t1t2=(2vsin⁡θ)(2vcos⁡θ)g2⇒2g[v2(2sinθcosθ)g]=2gv2sin2θg=2g=⇒2g[v2(2sin⁡θcos⁡θ)g]=2gv2sin⁡2θg=2g=RR∴t1t2∝R