Two projectiles are thrown simultaneously in | vedclass

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(B) Let the velocities of the two projectiles be $\vec{v}_1 = v_1 \cos 	heta_1 \hat{i} + v_1 \sin 	heta_1 \hat{j}$ and $\vec{v}_2 = v_2 \cos 	heta_

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a straight line

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(B) Let the velocities of the two projectiles be $\vec{v}_1 = v_1 \cos 	heta_1 \hat{i} + v_1 \sin 	heta_1 \hat{j}$ and $\vec{v}_2 = v_2 \cos 	heta_2 \hat{i} + v_2 \sin 	heta_2 \hat{j}$.Both projectiles experience the same acceleration due to gravity,$\vec{a}_1 = \vec{a}_2 = -g \hat{j}$.The relative acceleration of particle $1$ with respect to particle $2$ is $\vec{a}_{12} = \vec{a}_1 - \vec{a}_2 = 0$.Since the relative acceleration is zero,the relative velocity $\vec{v}_{12} = \vec{v}_1 - \vec{v}_2$ is constant.The relative velocity is $\vec{v}_{12} = (v_1 \cos 	heta_1 - v_2 \cos 	heta_2) \hat{i} + (v_1 \sin 	heta_1 - v_2 \sin 	heta_2) \hat{j}$.Since the relative acceleration is zero and the relative velocity is constant,the relative position vector $\vec{r}_{12} = \vec{v}_{12} t$ represents a straight line equation in the $xy$-plane.

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles $\theta_1$ and $\theta_2$ respectively from the horizontal,then the trajectory of particle $1$ with respect to particle $2$ will be:

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