Question

Starting from one corner of a cube an insect has to travel to the diagonally opposite corner. The insect travels along the edges. It transverses the first edge ab with constant velocity v1, the second edge bc with constant velocity v2 and the third edge cd with constant v3. Find the average velocity of the whole path

Answer 1

Answer:

√3 V₁V₂V₃ /(V₂V₃ + V₁V₃ + V₁V₂)

Explanation:

ab  = bc  = cd  = d

Time along ab = d/V₁

Time Along bc = d/V₂

Time along cd = d/V₃

Total Time = d/V₁ + d/V₂ + d/V₃

= d(V₂V₃ + V₁V₃ + V₁V₂)/(V₁V₂V₃)

Displacement = ad = √ab² + bc² + cd²

= √d² + d² + d²

= √3d

Average Velocity = √3d/{d(V₂V₃ + V₁V₃ + V₁V₂)/(V₁V₂V₃)}

= √3 V₁V₂V₃ /(V₂V₃ + V₁V₃ + V₁V₂)