Two straight wires AB and CD intersect each other at point O at an angle 37∘. They are moving parallel to themselves with the speeds v1=2ms−1 and v2=5ms−1.The speed of intersection point is 5(n)12ms−1. Find the value of n.

Let us suppose that straight wires AB and CD cross each other at point O at t = 0. At instant t, crossing point is at O as shown in figureDraw perpendiculars ON and OM on the displaced positions of the line. ThenON=v1t, OM=v2t, OO′=vtHere, OO′ is the diagonal of parallelogram  OEO'F.Here, OE=ONcosec⁡α=v1tcosec⁡αOF=OMcosec⁡α=v2tcosec⁡α∴ OO′=(OE)2+(OF)2+2(OE)(OF)cos⁡αor (vt)=v1tcosec⁡α2+v2tcosec⁡α2+2v1tcosec⁡αv2tcosec⁡αcos⁡α∴ v=v12+v22+2v1v2cos⁡αcosec⁡α∴ v=(4+25+2×2×5×45)53 m/s=5329+16 m/s=5345 m/s=55ms-1