Question

A man 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 did the drunkard takes to fall in a pit 13 m away from the start.

Answer 1

Distance covered in one step = 1 m

Time required for one step = 1 s

Distance for pit from initial position = 13 m

Time taken by drunkard to move 5m forward = 5 s

Time taken by drunkard to move 3m backward = 3 s

Speed of the drunkard = 1 m/s (∵from above two observations)

Net distance covered = 5-3 = 2 m

Net time required to cover 2m = 8 s

Total 6 complete forward-backward cycles possible.

Time taken for 6 cycles = 48 s

Distance covered in 6 cycles = 12 m

∴ Total time required to cover 13 m = 48 + 1 =49 s

The graph obtained from above data is,

Answer 2

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Distance covered with 1 step = 1 m

Time taken = 1 s

Time taken to move first 5 m forward = 5 s

Time taken to move 3 m backward = 3 s

Net distance covered = 5 – 3 = 2 m

Net time taken to cover 2 m = 8 s

Drunkard covers 2 m in 8 s.

Drunkard covered 4 m in 16 s.

Drunkard covered 6 m in 24 s.

Drunkard covered 8 m in 32 s.

In the next 5 s, the drunkard will cover a distance of 5 m and a total distance of 13 m and falls into the pit.

Net time taken by the drunkard to cover 13 m = 32 + 5 = 37 s

✊(GRAPH IN ATTACHMENT)

I hope, this will help you

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