Two particles having position vectors $$r1$$→$$=(3i^+5j^)$$ meters and $$r2$$→$$=($$−$$5i^$$−$$3j^)$$ meters are moving with velocities v→$$1=(4i^+3j^)$$ $$m/s$$ and v→$$2=($$α $$i^+7j^)m/s$$. If they collide after $$2$$ seconds, the value of 'α' is

Question

Two particles having position vectors $$r1$$→$$=(3i^+5j^)$$ meters and $$r2$$→$$=($$−$$5i^$$−$$3j^)$$ meters are moving with velocities v→$$1=(4i^+3j^)$$ $$m/s$$ and  v→$$2=($$α $$i^+7j^)m/s$$. If they collide after $$2$$ seconds, the value of  'α' is

Infinity Learn · Accepted Answer

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$$=8$$

Two particles having position vectors r1→=(3i^+5j^) meters and r2→=(−5i^−3j^) meters are moving with velocities v→1=(4i^+3j^) m/s and v→2=(α i^+7j^)m/s. If they collide after 2 seconds, the value of 'α' is

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