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.

A drunkard walking in a narrow lane takes 5 steps forward and 3 steps

1.	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» Solution : DISTANCE covered in each step =1 m Time TAKEN to cover each step =1 s Time taken to complete 5 step = 5 s Time taken to complete 5 forward STEPS and 3 backward steps = 8 s Effective distance covered `=5 -3=2` Similarly, effective distance covered in first 16 steps `=2 +2 = 4m` Total time taken for it = 16 is Similary, effective distance covered in first 24 steps, `= 2 + 2 + 2= 6M` Total time taken for it = 24 s Effective distance covered in first 32 steps, `= 2 + 2 + 2 + 2= 8m` Total time taken for it = 32 s Distance covered in first 37 steps Distance covered in 32 steps + distance covered in 5 steps. Thus, time taken to complete 13 m is 37 s. Hence , he will fall into pit in 37 s.