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99 Percentile Qs Bank for JEE MainPhysicsMotion in One Dimension

A 2 m wide truck is moving with a uniform speed v 0 = 8 m s - 1 along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v moving in a straight line, when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is

Options

  1. A6 5 m s - 1
  2. B4 5 m s - 1
  3. C8 5 m s - 1
  4. D2 5 m s - 1

Correct answer

C. 8 5 m s - 1

Step-by-step solution

Let the man starts crossing the road at an angle θ 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 + 2 cot θ. ​ ∴ 4 + 2 cot θ 8 = 2 / sin θ v or v = 8 2 sin θ + cos θ ...(1) For minimum v, dv d θ = 0 or - 8 2 cos θ - sin θ ( 2 sin θ + cos θ ) 2 = 0 or 2 cos θ - sin θ = 0 or tan θ = 2 from Equation (1) v min = 8 2 ( 2 5 ) + 1 5 = 8 5 m s - 1

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