Question

ravi wants to cross a wide road.At what angle with the edge of the road should he walk so that he walks the shortest distance​

Answer 1

Answer:

90° as perpendicular is always the shortest distance

Answer 2

Hence ravi should walk at 90 deg angle to edge of road to cross the road with shortest distance

Step-by-step explanation:

Let say Ravi walk at an angle of α

and distance covered = d

Then Horizontal distance = d Cosα

& Vertical distance = d sinα

d sinα = w   =  width of road

=> d²sin²α = w²

d² = d²Cos²α + d²sin²α

d²  = d²cos²α  + w²

as w² is constant   ( width of road)

hence to minimize d²   ,

d²cos²α should be minimum  

d²cos²α  = 0

=> cos²α  = 0

=> cosα = 0

=> α = 90°

Hence ravi should walk at 90 deg angle to edge of road to cross the road with shortest distance

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