Two particles A and B start simultaneously from the same point and move in a horizontal plane. A has an initial velocity u1 due east and acceleration a1 due north. B has an initial velocity u2 due north and acceleration a2 due east. Then :

Engineering

Physics

Straight Line Motion

Question

Two particles A and B start simultaneously from the same point and move in a horizontal plane. A has an initial velocity u₁ due east and acceleration a₁ due north. B has an initial velocity u₂ due north and acceleration a₂ due east. Then :

If u₁ > u₂ & a₁ < a₂, the particles will have the same speed at some point

They will collide only if a₁u₁ = a₂u₂

Their paths must intersect at same point

They must collide at some point

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$u_{1} t = \frac{1}{2} a_{2} t^{2}$

$u_{2} t = \frac{1}{2} a_{1} t^{2}$

$\frac{u_{1}}{u_{2}} = \frac{a_{2}}{a_{1}}$

$u = \sqrt{u_{1}^{2} + a_{1}^{2} t^{2}}$

$v = \sqrt{u_{2}^{2} + a_{2}^{2} t^{2}}$