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

Question

Infinity Learn · Accepted Answer

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$$ θ$$) $$4+2cot$$θ$$8=2/$$$$sin$$θv or   $$v=82sin$$θ$$+$$$$cos$$θ  For minimum v,dvdθ$$=0$$ $$-8(2cos$$θ$$-$$$$sin$$θ$$)(2sin$$θ$$+$$$$cos$$θ$$)2=0$$   or   $$2cos$$θ$$-$$$$sin$$θ$$=0$$ $$tan$$θ$$=2$$, so $$sin$$θ$$=25$$,$$cos$$θ$$=15$$ $$vmin=8225+15=85=3.57$$ $$ms-1$$

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

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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

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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