Question

two bodies are projected at angle theta and (90-theta)to the horizontal with the same speed. Find the ratio of their time of flight

Answer 1

that's the answer hope it helps you

Answer 2

The answer to the question is $\ tan\theta$ : 1

CALCULATION:

As per the question , the two bodies are projected at an angle $\theta\ and\ (90-\theta)$ with respect to horizontal.

Let us consider the initial velocity of the two projectiles is u .

The total time of flight of the first projectile is calculated as -

                          Time of flight $T_{1} =\ \frac{2usin\theta}{g}$ [1]

Here, g is the acceleration due to gravity.

The time of flight of the second projectile is calculated as -

                Time of flight $T_{2} =\ \frac{2usin(90-\theta)}{g}$

                                              $=\ \frac{2ucos\theta}{g}$   [ $sin(90-\theta)=\ cos\theta$     [2]

Dividing 1 by 2, we get-

                                   $\frac{T_{1}} {T_{2}}=\ \frac{2usin\theta/g}{2ucos\theta/g}$

                                          $=\ tan\theta$             [  $\frac{sin\theta}{cos\theta} =\tan\theta$  ]

                                  ⇒ $T_{1}:T_{2}=\ tan\theta :1$                                                                                                               [ans]