Two projectiles are thrown with the same init | vedclass

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Question

(C) The horizontal range $R$ of a projectile is given by the formula $R = \frac{u^2 \sin(2	heta)}{g}$,where $u$ is the initial velocity,$	heta$ is t

Vedclass · Accepted Answer

$2: \sqrt{3}$

Vedclass · Answer

(C) The horizontal range $R$ of a projectile is given by the formula $R = \frac{u^2 \sin(2	heta)}{g}$,where $u$ is the initial velocity,$	heta$ is the angle of projection,and $g$ is the acceleration due to gravity.Given $u$ is the same for both projectiles,the ratio of their ranges is $\frac{R_1}{R_2} = \frac{\sin(2	heta_1)}{\sin(2	heta_2)}$.For $	heta_1 = 45^{\circ}$,$2	heta_1 = 90^{\circ}$,so $\sin(90^{\circ}) = 1$.For $	heta_2 = 30^{\circ}$,$2	heta_2 = 60^{\circ}$,so $\sin(60^{\circ}) = \frac{\sqrt{3}}{2}$.Therefore,$\frac{R_1}{R_2} = \frac{1}{\sqrt{3}/2} = \frac{2}{\sqrt{3}}$.Thus,the ratio is $2: \sqrt{3}$.

Two projectiles are thrown with the same initial velocity making an angle of $45^{\circ}$ and $30^{\circ}$ with the horizontal,respectively. The ratio of their respective ranges will be:

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