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The distance between two moving cars A and B at a particular time is d. Their relative velocity is V with the component along AB being u and perpendicular to AB being v.The time that elapses before they arrive at their nearest distance is (A)du/V² (B) dv/V² (C)d(u+v)/V² (D)dV/(u+v)²

The distance between two moving cars A and B at a particular time is d. Their relative velocity is V with the component along AB being u and perpendicular to AB being v.The time that elapses before they arrive at their nearest distance is 
(A)du/V²   (B) dv/V²  (C)d(u+v)/V²   (D)dV/(u+v)²

Grade:11

1 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
3 years ago
Assuming P to be at rest, particle Q is moving with velocity vr,in the direction shown in figure.

Components of vr along and perpendicular to PQ are u and v respectively,

In the figure

sinα=u / vr

cosα = u / vr

The closest distance between the particles is

S min = PR = PQ = cosα = (a) (v / vr)

S min = av / vr

Time after which they arrive at their nearest distance is

t=QR / vr

= (PQ) sinα / vr

= (a)(v / vr)vr

=au / v^2r

The minimum distance between the two moving particles is au / v^2r.

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