Two straight roads intersect at O making angle α. Cars A and B are initially distances L₁ and L₂ from O and approach O with speeds v₁ and v₂. The unrestricted closest-approach time is:
Options

Question

Two straight roads intersect at O making angle α. Cars A and B are initially distances L₁ and L₂ from O and approach O with speeds v₁ and v₂. The unrestricted closest-approach time is:

G1 Physics · Accepted Answer

d²=(L₁−v₁t)²+(L₂−v₂t)²−2(L₁−v₁t)(L₂−v₂t)cosα. Differentiating and setting d(d²)/dt=0 gives option B.