Question

Two particles $A$ and $B$ are projected simultaneously from a point situated on a horizontal place. 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:

• A. $50m{s}^{-1},100m/s$
• B. $100m{s}^{-1},50m/s$
• C. $v_A$ can have any value greater than a certain value, $100m{s}^{-1}$
• D. none of these

Answer 1

Answer: (C)

Velocity of $A$ is always in vertical direction. At $5s$, velocity of $B$ is perpendicular to that of $A$. It means velocity of $B$ is horizontal or $B$ is at highest point.

Time of ascent $=\frac{v_{B}sin30^0}{g}=5s$

Now velocity of $A$ can have any value provided its time of flight is more than $5s$.

For this $v_A\ge 25m/s$