question_answer 4)

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:

(a) Graphical method. Taking the starting point as origin, the positions of the drunkard at various instants of time are given in the following table.                

t(s)	0	5	8	13	16	21	24	29	32	37
x(m)	0	5	2	7	4	9	6	11	8	13

   The position-time (x-t) graph for the motion of the drunkard is shown in Fig. 3.84. As is obvious from graph that the drunkard would take 37 s to fall in a pit 13 m away from the starting point.   Fig. 3.84 (b) Analytical method. In each forward motion of 5 steps and backward motion of 3 steps, net distance covered = 5 - 3 = 2 m and time taken = 5 + 3 = 8 s.  Time required to cover a distance of 8 m   Remaining distance of the pit In next 5 s, as he moves 5 steps forward, he falls into the pit.  Total time taken .