Question

Two particles are projected simultaneously in a vertical plane from the same point. These particles have different velocities at different angles with the horizontal. The path seen by each other is

• A. parabola
• B. hyperbola
• C. elliptical
• D. straight line

Answer 1

Answer: (D)

straight line

Here, $\overrightarrow{v_1}=\left(u_1\cos {\alpha }_1\right)\hat{i}+(u_1\sin {\alpha }_1-gt)\hat{j}$
and $\overrightarrow{v_2}=\left(u_1\cos {\alpha }_2\right)\hat{i}+(u_2\sin {\alpha }_2-gt)\hat{j}$
Relative velocity $\overrightarrow{v_{12}}=\overrightarrow{v_1}-\overrightarrow{v_2}$ has horizontal as well as vertical components and it is constant also, so that the path seen by each other is straight line with angle not equal to ${90}^{\circ }$