Answer to Question #80670 in Physics for Sahil

Question

A projectile can have the same range R for two angles of projection. If t1 and t2 be the time of flight in two cases,then prove that t1.t2=2R/g

Answer 1

We have:
R=(2U^2)/g sin⁡2ϴ
Projectile can have same range for angles of projection ϴ and 90-ϴ.
t_1=2Usinϴ/g
t_2=2Usin(90-ϴ)/g=2Ucosϴ/g
Then,
t_1 t_2=2Usinϴ/g 2Ucosϴ/g=(4U^2 sinϴcosϴ)/g^2 =(2U^2 sin⁡2ϴ)/g^2 =2R/g