Question

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 answer the following questions: If $v_1$ = $v_2$ and ${\theta }_1>{\theta }_2$, then choose the incorrect statement

• A. Particle 2 moves under the particle 1
• B. The slope of the trajectory of particle 2 with respect to 1 is always positive
• C. Both the particles will have the same range if ${\theta }_1>{45}^{\circ }$ and ${\theta }_2<{45}^{\circ }$ and ${\theta }_1+{\theta }_2$ = ${90}^{\circ }$
• D. none of these

Answer 1

The correct option is B

The slope of the trajectory of particle 2 with respect to 1 is always positive

Initial velocity of 2 w.r.t. 1: $V_{2/1}=(v_{2}cos{\theta }_2-v_{1}cos{\theta }_1)\hat{i}+(v_{2}sin{\theta }_2-v_{1}sin{\theta }_1)\hat{j}$

Its $\hat{i}$ part is positive and $\hat{j}$ part is negative.

Trajectory of particle 2 will be a straight line OA w.r.t 1 as shown. Its slope is negative.

Line 1 - 2 will be parallel to OA at any time.