A 2-m wide truck is moving with a uniform speed v0 = 8 ms-1 along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is

Let the man start crossing the road at an angle 0 with the roadside. For safe crossing, the condition is that the man must cross the road by the time the truck describes the distance (4 + 2 cot θ) 4+2cotθ8=2/sinθv or   v=82sinθ+cosθ  For minimum v,dvdθ=0 -8(2cosθ-sinθ)(2sinθ+cosθ)2=0   or   2cosθ-sinθ=0 tanθ=2, so sinθ=25,cosθ=15 vmin=8225+15=85=3.57 ms-1