# 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.

Given,

Distance covered in one step = 1 m

Time required for one step = 1 s

Distance for pit from initial position = 13 m

Time taken to move 5 m forward = 5 s

Time taken to move 3 m backward = 3 s

Speed of the drunkard = 1 m/s (from above two observations)

Net distance covered = 5-3 = 2 m

Net time required to cover 2 m = 8 s

Total 4 complete forward-backward cycles  and  5 forward steps is possible

Time taken for 4 cycles = 32  sec

Distance covered in 4 cycles = 32 m

Total time required to cover 13 m = 32 +5  = 37 s

The graph obtained from above data is,

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