Q.
Two particles 1 and 2 are projected with same speed $v$ as shown in figure. Particle 2 is on the ground and particle 1 is at a height $h$ from the ground and at a horizontal distance $s$ from particle 2. If a graph is plotted between $v$ and $s$ for the condition of collision of the two then ($v$ on $y$-axis and $s$ on $x$-axis)
A) It will be a parabola passing through the origin
B) It will be straight line passing through the origin and having a slope of $\sqrt{\frac{g}{8h}}$
C) It will be a straight line passing through the origin and having a slope of $\sqrt{\frac{g}{4h}}$
D) It will be a straight line not passing through the origin
Explanation
(b) Assuming particle 2 to be at rest, substituting in
$y = x\tan\theta - \frac{gx^{2}}{2u^{2}\cos^{2}\theta}\ \ \ (\theta = 0{^\circ})$
[image:4_image113.emf]
We have $- h = \frac{- g}{2(4v^{2})}$
or $v = \sqrt{\frac{g}{8h}}$
Which is a straight line passing through origin with slope $\sqrt{\frac{g}{8h}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.