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Two particles A and B are moving with un...

Two particles `A and B` are moving with uniform velocity as shown in (Fig. 5.130) given below at `t = 0`.
(a) Will the two particles collide ?
(b) Find out the shortest distance between two particles.
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Text Solution

Verified by Experts

Observing `A` from the frame of `B`
Let us draw `vec v_(A B)`,
`vec v_(A B) = vec v_A - vec v_B = vec v_A + (- vec v_B)`
`tan theta = (10)/(20) = (1)/(2)`
Again `tan theta = (A D)/(C D) = (A D)/(40) = (1)/(2)`
`rArr AD = 20 rArr D O = 10`
`rArr BC = 10`
Hence, the shortest distance between the particles
`d_("short") = BC cos theta = 10 cos theta = (10 xx 2)/(sqrt(5)) = 4 sqrt(5) m`
Since the closest distance is non - zero, therefore, the particles will not collide.
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