Two particles projected form the same point with same speed u at angles of projection `alpha and beta` strike the horizontal ground at the same point. If `h_1 and h_2` are the maximum heights attained by the projectile, R is the range for both and `t_1 and t_2` are their times of flights, respectively, then

Options

A. `alpha + beta = (pi)/(2)`
B. `R = 4 sqrt(h_(1)h_(2))`
C. `tan alpha = (t_(1))/(t_(2)) = sqrt(h_(1)h_(2))`
D. None of the above

Answer

D

Explanation

(a) Range becomes equal at complimentary angle. Hence
`beta = 90^(@) - alpha`
(b) `h_(1) = (u^(2) sin^(2)alpha)/(2g)`
`rArr h_(2) = (u^(2)cos^(2)alpha)/(2g)` (as `beta = 90 - alpha)`
`:. 4sqrt(h_(1)h_(2)) = (2u^(2)sin alpha cos alpha)/(g) = (u^(2)sin 2 alpha)/(g) = R`
(c) `(t_(1))/(t_(2)) = ((2u sin alpha//g))/((2u cos alpha//g)) = tan alpha`
(d) `sqrt((h_(1))/(h_(2))) = tan alpha`