Question

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.

Answer 1

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 

The x-t graph of the drunkard’s motion can be shown as: