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(D) For two projectiles with the same initial velocity $v$ and different angles $	heta_1$ and $	heta_2$,the equations of motion are $x_1 = v \cos

Vedclass · Accepted Answer

None of these.

Vedclass · Answer

(D) For two projectiles with the same initial velocity $v$ and different angles $	heta_1$ and $	heta_2$,the equations of motion are $x_1 = v \cos 	heta_1 t$,$y_1 = v \sin 	heta_1 t - \frac{1}{2}gt^2$ and $x_2 = v \cos 	heta_2 t$,$y_2 = v \sin 	heta_2 t - \frac{1}{2}gt^2$.Since $	heta_1 > 	heta_2$,we have $\cos 	heta_1  0$. Also,the relative vertical position is $y_1 - y_2 = v t (\sin 	heta_1 - \sin 	heta_2)$. Since $	heta_1 > 	heta_2$,$\sin 	heta_1 > \sin 	heta_2$,so $y_1 > y_2$. This means particle $1$ is always above particle $2$,so particle $2$ moves under particle $1$. The slope of the relative trajectory is $\frac{dy_1 - dy_2}{dx_1 - dx_2}$,which remains positive under these conditions. Option $C$ is a general property of complementary angles,but the question asks for the incorrect statement regarding the specific condition $	heta_1 > 	heta_2$. Since $A$ and $B$ are correct,and $C$ is a true statement about range,$D$ is the correct choice as there is no incorrect statement among the given options.

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