Two particles A and B are projected simultaneously from points P and Q respectively as shown in figure. Particle A was projected vertically while particle B was projected horizontally. If horizontal a

Question

Two particles A and B are projected simultaneously from points P and Q respectively as shown in figure. Particle A was projected vertically while particle B was projected horizontally. If horizontal and vertical component of PQ are 27 m and 45 m respectively then find the minimum value of $V_{B}$ in m/s for which a collision is possible between A and B.

TestHub · Accepted Answer

Writing position of A and B at time t.

For $A, x = 0; y = V_{A} t - \frac{1}{2} gt^{2}$

For $B : x = 27 - V_{B} t; y = 45 - \frac{1}{2} gt^{2}$

For collision both particle must be at a same place in air $\Rightarrow V_{A} t = 45 \Rightarrow V_{B} t = 27$ Now, $y_{Q} > 0 \Rightarrow 45 - 5 t^{2} > 0 \Rightarrow t < 3 sec . \Rightarrow V_{B} = \frac{27}{3} = 9 m / s$

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