Question

Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal, respectively. The ratio of their respective ranges will be

• A. $1 : \sqrt2$
• B. $\sqrt2 : 1$
• C. $2 : \sqrt3$
• D. $\sqrt3 : 2$

Answer 1

Answer: (C)

$2 : \sqrt3$

Answer 2

The ratio of their respective ranges with angles of** ** $45\degree and \;30\degree$

$\Rightarrow \frac{ R_1}{R_2}$ $\bigg[R = \frac{u^2 sin 2θ}{g}\bigg]$

= $\frac{sin 2θ_1}{ sin 2θ_2}$

= $\frac{1}{\frac{\sqrt3}{2}}$

= $\frac{2}{\sqrt3}$

Hence, the correct option is (C): $\frac{2}{\sqrt3}$