Question

What is the relationship between time of flight $T$ and horizontal range $R$?
(where $\theta$ is angle of projection with the horizontal)

• A. $R=\frac{gT}{\tan \theta }$
• B. $R=\frac{g{T}^2}{2\tan \theta }$
• C. $R=\frac{g{T}^2}{\tan \theta }$
• D. $R=\frac{gT}{2\tan \theta }$

Answer 1

The correct option is B $R=\frac{g{T}^2}{2\tan \theta }$

Time of flight in projectile motion is given by

$T=\frac{2usin\theta }{g}$. . . . . . .(1)

Horizontal range in projectile motion

$R=\frac{u^{2}sin2\theta }{g}$. . . . .(2)

From equation $\left(1\right)$ and $\left(2\right)$, we get

$R=\frac{{\left(\frac{Tg}{2sin\theta }\right)}^{2}sin2\theta }{g}$

$R=\frac{T^2{g}^{2}2sin\theta cos\theta }{usi{n}^2\theta .g}$

$R=\frac{T^{2}g}{2tan\theta }$

The correct option is B.