Two particles are projected from the same point with the same speed, at different angles θ 1 and θ 2 to the horizontal. They have the same horizontal range. Their times of flight are t 1 and t 2

Question

Two particles are projected from the same point with the same speed, at different angles θ 1 ​ and θ 2 ​ to the horizontal. They have the same horizontal range. Their times of flight are t 1 ​ and t 2 ​ respectively.

TestHub · Accepted Answer

Same speed and same horizontal range means the two angles are complementary.

$θ_{1} + θ_{2} = 9 0^{\circ}$ - (A) is correct.

Time of flight: $t = \frac{2 u s i n θ}{g}$

$\frac{t _{1}}{t _{2}} = \frac{s i n θ _{1}}{s i n θ _{2}} = \frac{s i n θ _{1}}{c o s θ _{1}} = tan θ_{1}$ - (B) is correct, (C) is wrong.

$\frac{t}{s i n θ} = \frac{2 u}{g}$ is the same for both particles, so $\frac{t _{1}}{s i n θ _{1}} = \frac{t _{2}}{s i n θ _{2}}$ - (D) is correct.

Physics - Kinematics Question with Solution | TestHub

Options:(select one or more)

Doubts & Discussion