Question

g If you keep the launch angle fixed, but double the initial launch speed, what happens to the range?

Answer 1

Answer:

Range will become 4 times of initial range

Explanation:

Let the velocity of projection is u

And angle at which projectile is projected is $\Theta$

And acceleration due to gravity is $g\ m/sec^2$

So range of projectile is equal to $R=\frac{u^2sin2\Theta }{g}$........eqn 1

Now in second case it is given that velocity of launching is doubled

So new velocity $u_{new}=2u$

So new range will be equal to $R_{new}=\frac{(2u)^2sin2\Theta }{g}=\frac{4u^2sin2\Theta }{g}$ .....eqn 2

Now dividing eqn 2 by eqn 1

$\frac{R_{new}}{R}=\frac{4u^2sin2\Theta }{g}\times \frac{g}{u^2sin2\Theta }$

$R_{new}=4R$

So if we double the initial launch speed then range will become 4 times