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.
Given: A drunkard 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 takes 1 s .
Time taken to move first 5 m forward is 5 s .
Time taken to move 3 m backward is 3 s .
Net distance covered is,
5 − 3 = 2 m
Net time taken to cover 2 m is,
5 + 3 = 8 s
Hence, the drunkard covers 2 m in 8 s .
Time taken to cover 4 m is 16 s .
Time taken to cover 6 m is 24 s .
Time taken to cover 8 m is 32 s .
In the next five steps, the drunkard covers a distance of 5 m and a total distance of 13 m and falls into the pit.
Thus, net time taken by the drunkard to cover 13 m is 32 + 5 = 37 s .
The x-t graph of the drunkard’s motion is shown below.
Given: A drunkard takes
Time taken to move first
Time taken to move
Net distance covered is,
Net time taken to cover
Hence, the drunkard covers
Time taken to cover
Time taken to cover
Time taken to cover
In the next five steps, the drunkard covers a distance of
Thus, net time taken by the drunkard to cover
The x-t graph of the drunkard’s motion is shown below.
