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, thenA. `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

Two particles projected form the same point with same speed u at angle

1.	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, thenA. `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» Correct Answer - D (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`