Two projectiles are fired from the same point | vedclass

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(B) 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 speed and $	heta$ is

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Their range will be same

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(B) 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 speed and $	heta$ is the angle of projection.For the first projectile: $	heta_1 = 60^\circ$. Thus,$R_1 = \frac{u^2 \sin(2 	imes 60^\circ)}{g} = \frac{u^2 \sin(120^\circ)}{g} = \frac{u^2 \sin(60^\circ)}{g} = \frac{u^2 \sqrt{3}}{2g}$.For the second projectile: $	heta_2 = 30^\circ$. Thus,$R_2 = \frac{u^2 \sin(2 	imes 30^\circ)}{g} = \frac{u^2 \sin(60^\circ)}{g} = \frac{u^2 \sqrt{3}}{2g}$.Since $\sin(2 	imes 60^\circ) = \sin(120^\circ) = \sin(60^\circ) = \sin(2 	imes 30^\circ)$,the ranges are equal when the sum of the angles is $90^\circ$ (complementary angles). Therefore,their range will be same.

Two projectiles are fired from the same point with the same speed at angles of projection $60^\circ$ and $30^\circ$ respectively. Which one of the following is true?

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