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Q.

A 2m wide truck is moving with a uniform speed v0 = 8m/s 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 p5m/s. The value of p is

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answer is 8.

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Detailed Solution

For safe crossing, the condition is that the man must cross the road by the time the truck covers the distance 4 + AC or 4 + 2cotθ∴ 4+2cot⁡θ8=2/sin⁡θv⇒v=82sin⁡θ+cos⁡θ For minimum v,dvdθ=0 ⇒ tan⁡θ=2vmin=85m/s
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A 2m wide truck is moving with a uniform speed v0 = 8m/s 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 p5m/s. The value of p is