A cannon ball has a range Ron a horizontal plane, such that the corresponding possible maximum heights reached are H_1 and H_2 . Then, the correct expression for R is

A cannon ball has a range Ron a horizontal plane, such that the corres

1.	A cannon ball has a range Ron a horizontal plane, such that the corresponding possible maximum heights reached are H_1 and H_2 . Then, the correct expression for R is
Answer» `((H_(1)) +H_(2))/2` `(H_1H_2)^2` `2(H_1H_2)^(1//2)` `4(H_1H_2)^(1//2)` Solution :The CANNON ball will have same horizontal RANGE for angle of projection `theta and (90^(@) - theta)` . So `H_1=(u^2 sin^(2) theta)/(2g) and H_2 =(u^2 sin^(2) (90^@ - theta))/(2g)=(u^2 cos ^(2) theta)/(2g)` `:. H_1H_2 =1/4 ((u^2 sin thetacos theta)/(g))^2=1/4xxR^2/4 ( :. R=(u^2 sin 2 theta)/g)` `R=4sqrt(H_1H_2)`