Question

Two bodies are projected at angles θ and (90⁰−θ) to the horizontal with the same speed. The ratio of their times of flight is

• A. $\sin \theta :1$
• B. $\cos \theta :1$
• C. $\sin \theta :\cos \theta$
• D. $\cos \theta :\sin \theta$

Answer 1

The correct option is C

$\sin \theta :\cos \theta$

Step 1: Given:

Projection angle of the first body ${\theta }_1=\theta$

Projection angle of the second body ${\theta }_2={90}^{°}-\theta$

Step 2: To find:

The ratio of their times of flight.

Step 3: Calculte ratio of times of flight:

The time of flight is given by

$T=\frac{2u\sin \theta }{g}$

Here, $u$ is the initial velocity,$\theta$ is the projectile angle, and $g$ is the gravitational acceleration.

$T\propto \sin \theta$ (As both the projectile is projected with the same initial speed u, and the value of g is constant.)

$$\begin{gathered} \frac{T_1}{T_2}=\frac{\sin {\theta }_1}{\sin {\theta }_2} \\ =\frac{\sin \theta }{\sin \left(90°-\theta \right)} \\ =\frac{\sin \theta }{\cos \theta } \end{gathered}$$

Hence, option(C) is correct.