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Grade upto college level General Physics

Two straight lines L₁ and L₂ cross each other at point P . The line L₁ is moving at a speed v₁ perpendicular to itself and line L₂ is moving at speed v₂ in the similar fashion. What will be the speed of point P?

Deepak Patra

12 Years agoGrade upto college level

1 Answer

Saurabh Koranglekar

6 Years ago

Let S be the point on L1 vertically below P. From ∆ONQ, sinθ=v2/OQ. From ∆QSP, tanθ=v1/QS.

OS=OQ+QS

=v2/sinθ+v1/tanθ

=(v2+v1cosθ)/sinθ.

OP^2=OS^2+SP^2

=(v2+v1cosθ)^2/(sinθ)^2+v1^2

=(v2^2+2v1v2cosθ+v1^2.(cosθ)^2

+v1^2.(sinθ)^2)/(sinθ)^2

=(v2^2+2v1v2cosθ+v1^2)/(sinθ)^2.

The speed of point P is

OP=√(v2^2±2v1v2cosθ+v1^2)/sinθ.

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