Question

Two stones a and b thrown at angle of theta and 90-theta with horizontal the ratio of their time of filght is

Answer 1

Concept : time of flight of any projectile is the time interval in which the projectile was in the air. Here, in this question, we are provided with the angle of projections of two stones a and b which are ∅ and (90 – ∅). By using the formula of time of flight we'll find their respective values and then find the ratio.

The time of flight of a projectile is calculated as:

$\\\quad\leadsto\quad\underline{\boxed{\sf T = \dfrac{2u\sin\theta}{g} }}\bigstar$

where, T, u, and g represent initial velocity, time of flight, initial velocity, and acceleration due to gravity respectively.

Assumption : let the time of flight for a be T₁ and time of flight for b be T₂

Now let's find the ratio:

$\\\quad\longrightarrow\quad\sf \dfrac{T_{1}}{T_{2}} = \bigg[\dfrac{2u\sin\theta}{g} \bigg]\div \bigg[\dfrac{2u\sin(90-\theta)}{g} \bigg]$

$\quad\longrightarrow\quad\sf \dfrac{T_{1}}{T_{2}} = \dfrac{2u\sin\theta}{g} \times \dfrac{g}{2u\cos\theta}$

$\quad\longrightarrow\quad \boxed{\bf \dfrac{T_{1}}{T_{2}} = \tan\theta}\bigstar$

hence, the required ratio is tan∅

That's the required answer!!