Question

A projectile has a time of flight t and range r if the time of flight is doubled keeping the angle of projection same then what will be the new range

Answer 1

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,
$t^2=\frac{4u^2sin^2\theta}{g^2}$......(1)
range , r = $\frac{u^2sin2\theta}{g}$
we know, $sin2\theta=2sin\theta.cos\theta$

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

dividing equation (2) by (1),
$\frac{r}{t^2}=\frac{g}{2}cos\theta$
e.g., $r\propto t^2$

here we can see that range of projectile is directly proportional to square of time of flight.
so, if the time of flight is doubled keeping the angle of projection same then, new range should be four times.

Answer 2

Answer:

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