1. Tardigrade
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  4. A drunkard walking in a narrow lane takes 8 steps forward and 6 steps backward, followed again by 8 steps forward and 6 steps backward and so on. Each step is 1 m long and requires 1 s. Determine how long the drunkard takes to fall in a pit 18 m away from the start

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Q. A drunkard walking in a narrow lane takes 8 steps forward and 6 steps backward, followed again by 8 steps forward and 6 steps backward and so on. Each step is 1 m long and requires 1 s. Determine how long the drunkard takes to fall in a pit 18 m away from the start

Motion in a Straight Line

Solution:

When the drunkard walks 8 steps forward and 6 steps backward, the displacement in the first 14 steps
$= 8\, m - 6\, m = 2\, m$
Time taken for first 14 steps $= 14\, s$
Time taken by drunkard to cover first 10 m of journey
$= \frac{14}{2}\times10 = 70\,s$
If the drunkard takes 8 steps more, he will fall into the pit, so the time taken by the last 8 steps $= 8 \,s$
Total time taken $= 70 \,s + 8\, s = 78\, s$