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Kinematics

Problem 1.16

Two particles, \(1\) and \(2,\) move with constant velocities \(v_{1}\) and \(v_{2}\) along two mutually perpendicular straight lines toward the intersection point \(O .\) At the moment \(t=0\) the particles were located at the distances \(l_{1}\) and \(l_{2}\) from the point \(O\). How soon will the distance between the particles become the smallest? What is it equal to?

Reveal Answer
tm=v1l1+v2l2v12+v22,lmin=∣l1v2−l2v1∣v12+v22t_{m}=\frac{v_{1} l_{1}+v_{2} l_{2}}{v_{1}^{2}+v_{2}^{2}}, \quad l_{m i n}=\frac{\left|l_{1} v_{2}-l_{2} v_{1}\right|}{\sqrt{v_{1}^{2}+v_{2}^{2}}}
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