A 2 ~m wide truck is moving with a uniform speed v₀=8 ~m / s along a straight horizontal road. A pedestrain 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

Step-by-step solution

Let the man starts crossing the road at an angle 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 । A C or 4 । 2 . 4+2 8 = 2 / v or v= 8 2 + For minimum v, d v d =0 or -8(2 - ) (2 + )² =0 or 2 - =0 or =2 From equation (i), v_ = 8 2 ( 2 5 )+ 1 5 = 8 5 =3.57 ~m / s