3.4 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 1m long and requires 1 s. Plot the xt graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.
3.4 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 1m long and requires 1 s. Plot the xt graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.
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1 Answer
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3.4

The time taken for each step is 1s, he covers 5 m in 5 secs and goes backward by 3 m in 3 secs.
So in 8 s he covers 2 m. To cover 13m distance he needs to complete 8 m (13-5). To cover 8m, he will require 8 * 4 = 32 s. To fall in a pit, he needs to move another 5m in 5s.
So total time taken = 32 +5 = 37 s
Let’s have a look at how we came to this answer.
We have to calculate how long it will take for the drunkard to fall into a pit located 13 metres from his starting point.
In each cycle of movement, the drunkard takes 5 steps forward and 3 steps backward. We calculate the net displacement per cycle.
Time for one cycle =
...more
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[P] = MLT-1
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