A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the `x -t` graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start

Explanation

It is clear from the x-t graph ,[Figure ], that the time taken by the drunkard to fall in the pit 13 m ways from the starts =37 s .
`x ubrace(5m+(-3m)) /(2m) +ubrace (5m+(-3m))/(2m) +ubrace (5m+(-3m))/(2m) +ubrace (5m+(-3m))/(2m) +5m =13m `
(Taking x as positive for forward direction and negative for the backward direction). Obviously, the number of steps involved and the time required for 37 steps is 37 s.
Aliter .
Displacement of the drunkard in first 8 steps Time required to take 8 steps = 8s
Average velocity `= ("Displacement ")/("time") =(2m)/(8s) =(1)/(4) m//s`
Neglecting the last 5 steps of 5m which would be taken only in the forward direction (as these would land the drunkard into the pit), total displacement of the drunkard before falling in the pit
Time required to cover 8m ` =("displacement")/("velocity") =(8m)/((t//4)m//s) ` = 32s
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