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

time	step distance
0	0	0
1	1	1
2	2	2
3	3	3
4	4	4
5	5	5
6	6	4
7	7	3
8	8	2
9	9	3
10	10	4
11	11	5
12	12	6
13	13	7
14	14	6
15	15	5
16	16	4
17	17	5
18	18	6
19	19	7
20	20	8
21	21	9
22	22	8
23	23	7
24	24	6
25	25	7
26	26	8
27	27	9
28	28	10
29	29	11
30	30	10
31	31	9
32	32	8
33	33	9
34	34	10
35	35	11
36	36	12
37	37	13

Lets call 1 cycle = going forward + coming back

In 1 cycle, he goes 2 steps = $2m$ forward

In 1 cycle, he spends time of 8 units

So, in 4 cycles, displacement $=8m$, time = 32 units

For 5th cycle, man reaches pit in 5 steps and falls in the pit

So, total time = $32+5=37$ units