Q. 44.2( 157 Votes )

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.

Answer :

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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