Question

Two particles $A$ and $B$ are projected simultaneously from a point situated on a horizontal plane. The particle $A$ is projected vertically up with a velocity $v_A$ while the particle $B$ is projected up at an angle of ${30}^{\circ }$ with horizontal with a velocity $v_B$. After $5s$, the particles were observed moving mutually perpendicular to each other. The velocity of projection of the particle $v_A$ and $v_B$ respectively are
(Take $g=10m/s^2$)

• A. $50m{s}^{-1},10m{s}^{-1}$
• B. $100m{s}^{-1},50m{s}^{-1}$
• C. $v_A$ can have any value greater than $25m{s}^{-1},100m{s}^{-1}$
• D. $20m{s}^{-1},100m{s}^{-1}$

Answer 1

The correct option is C $v_A$ can have any value greater than $25m{s}^{-1},100m{s}^{-1}$

Velocity of $A$ is always in the vertical direction. So, after $5s$ velocity of $B$ should be horizontal which happens when the projectile is at half the time of flight .
$\Rightarrow \frac{T}{2}=5$ or $T=10$ (where $T$ is the time of flight)
$\therefore T=\frac{2v_B\sin \theta }{g}=10$
or $v_B=100m/s$
Time of flight of $A$ should be greater than $5s$
$\Rightarrow \frac{2v_A\sin {90}^{\circ }}{g}>5$
$v_A>25m/s$