Let the man starts crossing the road at an angle θ as shown in figure. For safe crossing the condition is that the man must cross the road by the time the truck describes the distance 4 + AC or 4 + 2cot θ ∴
4+2cotθ
8
=
2∕sinθ
v
or v =
8
2sinθ+cosθ
... (i) For minimum v ,
dv
dθ
= 0
or
−8(2cosθ−sinθ)
(2sinθ+cosθ)2
= 0 or 2 cos θ - sin t = 0 or tan θ = 2 From equation (i), vmin =