Question

If for a given angle of projection ,the horizontal range is doubled,the time of flight becomes

Answer 1

Expression for time of flight,

$T=\dfrac {2u\sin\theta}{g}\quad\longrightarrow\quad (1)$

Expression for horizontal range,

$R=\dfrac {2u^2\sin\theta\cos\theta}{g}\quad\longrightarrow\quad (2)$

Dividing (2) by (1),

$\dfrac {R}{T}=u\cos\theta$

Since $\theta$ is fixed,

$T\propto\dfrac {R}{u}\quad\longrightarrow\quad (3)$

But from (2),

$u\propto\sqrt{R}$

Then (3) becomes,

$T\propto\sqrt R$

This means, if horizontal range is doubled, then time of flight becomes √2 times.