Two bodies are projected from the same points withequal speeds in such directions that they both strike the same point on a plane whose inclination is beta. If alpha be the anlge of projection of the first body with the horizontal show that the ratio of their times of light is (sin(alpha-beta))/(cos alpha)

Two bodies are projected from the same points withequal speeds in such

1.	Two bodies are projected from the same points withequal speeds in such directions that they both strike the same point on a plane whose inclination is beta. If alpha be the anlge of projection of the first body with the horizontal show that the ratio of their times of light is (sin(alpha-beta))/(cos alpha)
Answer» SOLUTION :Let `alpha` be the ANGLE of projection of the second body `R=(u^(2))/(g cos^(2)BETA)[sin(2 alpha-beta)-sin beta]` Range of both the bodies is same, therefore `sin (2alpha-beta)=sin(2 alpha.-beta)` or `sin 2 alpha.-beta=pi-(2alpha-beta)`, `alpha.=(pi)/2-(alpha-beta)` Now `T=(2U sin (alpha-beta))/(g cos beta)` and `T.=(2u sin (alpha.-beta))/(g cos beta)` `:.T/(T.)=(2SIN (alpha-beta))/(2sin (alpha.-beta))=(sin(alpha-beta))/(sin{(pi)/2-(alpha-beta)-beta})` `sin=((alpha-beta))/(sin((pi)/2-alpha))=(sin(alpha-beta))/(cos alpha)`