Question

A drunkard walking in a narrow lane takes 8 steps forward and 6steps backward,followed again by 8 steps forward and 6 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 18 m away from the start.

Answer 1

Solution :-

According to the given question ,

The drunkard moves 8 steps forward

Then he moves 6 steps backwards

Net distance traveled by the drunkard

= 8 -6 = 2 m

Net distance traveled by the drunkard = 2 m

The drunkard moves 8 steps forward and 6 steps backwards the total number of steps come out to be 14

As ,each step is 1m long and requires 1 second

Total time taken = 14 seconds

Hence , from this we can conclude that the total time required to cover a distance of 2 m is 14 seconds

Similarly ,

The drunkard covers 4m in 28 sec

The drunkard covers 6m in 42 sec

The drunkard covers 8m in 56 sec

The drunkard covers 10m in  70 sec

After covering a distance of 10 m when  the drunkard will move 8 steps forward the total distance will be 18 m and he will fall into the pit

Total time taken to cover a distance of 18 m

$\mathtt{= 70 +8}$

$\mathtt{= 78 sec }$

Total time taken by the drunkard to fall in the pit = 78 sec

Graph  :-

• As the drunkard repeats the same cycle throughout it's motion we can conclude that the distance covered by the drunkard in remains constant with respect to time .
• As a result the drunkard moves in uniform motion
• The graph of uniform motion is linear and has a uniform slope

pls refer the attachment