1. Tardigrade
  2. Question
  3. Physics
  4. 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 vA while the particle B is projected up at an angle of 30° with horizontal with a velocity vB. After 5 s the particles were observed moving mutually perpendicular to each other. The velocity of projection of the particle vA and vB respectively are:

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Q. 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 $5 s$ the particles were observed moving mutually perpendicular to each other. The velocity of projection of the particle $v_A$ and $v_{B}$ respectively are:

Motion in a Plane

Solution:

Velocity of $A$ is always in vertical direction. At $5 \,s$, 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 $=\frac{v_{B}\,\,sin \,30^{0}}{g}=5\, s$
Now velocity of $A$ can have any value provided its time of flight is more than $5\, s$.
For this $v_{A} \ge 25\, m/s$