Question

A projectile has a time of flight $T$ and range $R$. If the time of flight is double, what happens to the range?

• A. $\frac{R}{4}$
• B. $\frac{R}{2}$
• C. $2R$
• D. $4R$

Answer 1

The correct option is A $\frac{R}{4}$

The correct option is A.

Given,

Time of flight is $T$

$Range=R$

So, Let a particle is projected with speed $u$ at an angle $\theta$ with horizontal. after time $t$ particle strikes the ground.

so, time of flight,

$T=\frac{2usin\theta }{g}$

Squaring both sides,

$T^2=\frac{4u^{2}si{n}^2\theta }{g^2}......\left(1\right)$

Range , $R=\frac{u^{2}sin2\theta }{g}$

We know, $sin2\theta =2sin\theta .cos\theta$

$R=\frac{2u^{2}sin\theta cos\theta }{g}........\left(2\right)$

Dividing equation (2) by (1),

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

So, $R\propto T^2$

Thus, we can see that range of the projectile is directly proportional to the square of time of flight.

so, if the time of flight is doubled keeping the angle of projection same then, the new range should be four times.