Two particles are projected with speed 4 m/s and 3 m/s simultaneously from same point as shown in the figure. Then

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Their relative velocity is constant and has magnitude 1.4 m/s

Their relative velocity is along vertical direction is non zero

Their relative acceleration is non-zero and it is along vertical direction

They will hit the surface simultaneously

answer is C, D.

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Detailed Solution

$u_{y_{1}} = 4 \sin 37 = \frac{12}{5} m / \sec u_{y_{2}} = 3 \sin 53 = \frac{12}{5} m / \sec; {\vec{u}}_{r y} = \frac{12}{5} - \frac{12}{5} = 0$

So there is no relative velocity along vertical direction
${\vec{u}}_{x_{1}} = 4 \cos 37 = \frac{16}{5} m / \sec {\vec{u}}_{x_{2}} = 3 \sin 37 = \frac{9}{5} m / \sec {\vec{u}}_{r x} = \frac{16}{5} - \frac{9}{5} = \frac{7}{5} m / \sec$

So ${\vec{u}}_{r} = \frac{7}{5} \hat{i}$ (only horizontal) $= 1.4 m / \sec$