1.

A projectile can have same range `R` for two angles of projection. It `t_1 and t_2` are the times of flight in the two cases, then what is the product of two times of flight ?A. `t_1 t_2 prop R^2`B. `t_1 t_2 prop R`C. `t_1 t_2 prop (1)/( R)`D. `t_1 t_2 prop (1)/(R^2)`

Answer» Correct Answer - B
(b) The horizontal range is the same for the angles of projection `theta and (90^@ - theta)`.
`t_1 = (2 u sin theta)/(g), t_2 = (2 u sin (90^@ - theta))/(g) = (2 u cos theta)/(g)`
`t_1 t_2 = (2 u sin theta)/(g) xx (2 u cos theta)/(g) = (2)/(g) [(u^2 sin 2 theta)/(g)] = (2)/(g) R`
where `R = (u^2 sin 2 theta)/(g)`
Hence, `t_1 t_2 prop R` (as R is constant).


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