The distance between two moving particles at any time is a. If v be their relative velocity v1 and v2 be the components of v along and perpendicular to a. The minimum distance between them is?
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The minimum distance between the two moving particles is au / v^2r.
Explanation:
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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