Question

A projectile has a range R and time of flight T. If the range is doubled by increasing the speed of projection, without changing the angle of projection, the time of flight will become

• A. $\frac{T}{\sqrt{2}}$
• B. $\sqrt{2}T$
• C. $\frac{T}{2}$
• D. $2T$

Answer 1

The correct option is B

$\sqrt{2}T$

We know that, $R=\frac{v_0^{2}sin2{\theta }_0}{g}$
When the range is doubled without changing the angle of projection, the initial velocity becomes $\sqrt{2}$ times.
Now, $T=\frac{2v_{0}sin{\theta }_0}{g}=2\times \sqrt{\frac{Rg}{sin2{\theta }_0}}\times \frac{sin{\theta }_0}{g}$
As $T\propto \sqrt{R}$, the time of flight will become $\sqrt{2}$ times.
Hence, the correct choice is (b).