Question 1:
easy
Two particles are projected with same initial velocity one makes angle \(\theta\) with horizontal while other makes an angle \(\theta\) with vertical. If their common range is R then product of their time of flight is directly proportional to:
(1999)
Concept: Time of flight for complementary angles and range formula.
Formula: \(T = (2u sin \alpha) / g\), \(R = (u^2 sin 2\alpha) / g\).
For angles \(\theta\) and \(90° - \theta\), times are \(T_1 = (2u sin \theta) / g\) and \(T_2 = (2u cos \theta) / g\).
Their product \(T_1 T_2 = (4u^2 sin \theta cos \theta) / g^2 = (2u^2 sin 2\theta) / g^2 = (2/g) R\). Thus, \(T_1 T_2 \propto R\).