Please help me solve this random walk problem 4. An ant is taking a two-dimensio

Question

Please help me solve this random walk problem

4. An ant is taking a two-dimensional random walk on a flat surface. We will distinguish steps that the ant takes with its feet from the random walk (RW) steps, of length 5, which are made up of lots of footsteps. In a RW step, the ant choose a direction randomly and walks distance in that direction. She then choose another direction randomly and walks distance in that direction. She r surface conveniently has r- and y-co ant's progress along each direction, as well as the distance from the starting point The ant walks at a rate of 5cm/min and normally walks for 30s in each of its random walk steps ts this for a total of n RW steps. The ordinates drawn on it, so that we can monitor the epea (a) If the ant walks for 30 min, without stops to rest and always in segments of 30s, calculate the following: The total distance walked (as measured by a pedometer on one of its six legs) . The number of RW steps, n in a single walk. ·The distance covered, , in a single RW steps. (b) At the end of each n RW steps, the ant takes a rest for a few minutes and then starts off on another random walk of n steps. Assuming that the ant completes a lar number, N, of random walks, all the same, calculate the following: . The average (RMS) distance that the ant moves from the starting point of each walk . The average (RMS) distance that the ant moves from the starting point of each walk in the r-direction The expected total RMS distance from the original starting point after N random walks of n steps each. (This question assumes that the ant would be up to repeating all of the N random walks a large number of times, and the distance would be measured from the start of each set of N walks to the end of each set.) (c) It's not clear why the ant is doing all of this walking, but she seems to have become dissatisfied, and has changed her routine. Now, she walks in straight segments for

Explanation / Answer

I have solved first three solutions only as per chegg answering guideline.

Solution:

The total distance= Speed x total time

Speed = 5 cm/min

t = 30 min

total distance = 5 x 30 = 150 cm Or 1.50 m .......Ans

Distance covered in single RW ,

& = 5 cm/min x 30 s = 5 cm/ min x (30 / 60 min) = 2.5 cm ....Ans

number of steps = total distance / distance in RW step

n = 120 / 2.5 = 48 steps

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