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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.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
It is given that
Distance covered in one step = 1 m
Time taken = 1s
So the time is taken to move the first 5 steps forward = 5 s
Time is taken to move 3 steps backward = 3 s
Net distance covered = 5 – 3 = 2m
Net time is taken to cover 2 m = 8 s
So we get
Drunkard covers 2 m in 8s
Drunkard covers 4 m in 16s
Drunkard covers 6 m in 24s
Drunkard covers 8 m in 32s
In the next 5s drunkard will cover 5m and a total distance of 13m and fall into a pit
Net time taken by drunkard to cover 13m = 32 + 5 = 37s
x-t graph of the drunkard’s motion is shown as
Therefore, the drunkard takes 37s to fall into a pit 13 m away from the start.
Summary:
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 backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. The drunkard takes 37s to fall in a pit 13 m away from the start.
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