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Two particles having position vectors r1=(3i^+5j^) meters and r2=(5i^3j^) meters are moving with velocities v1=(4i^+3j^)m/s and  v2=(αi^+7j^)m/s. If they collide after 2 seconds, the value of  'α' is

a
2
b
4
c
6
d
8

detailed solution

Correct option is D

It is clear from figure that the displacement vector Δr→ between particles p1 and p2 is Δr→=r2→−r1→=−8i^−8j^ |Δr→| =(−8)2+(−8)2=82          …..(i)Now, as the particles are moving in same direction (∵ v1→ and v2→ are +ve), the relative velocity is given byv→rel=v2→−v1→=(α−4)i^+4j^v→rel=(α−4)2+16                           …..(ii)Now, we know  |v→rel| =|Δr→|tSubstituting the values of  v→rel and |Δr→| from equation (i) and (ii) and t=2s, then on solving we get  α=8

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