Question 34

Gita starts from point A and walks 1000 m east. She then walks 800 m north, followed by 640 m west and 512 m south, reaching point B. After this, she continues moving in the same cyclic order: east, north, west, south, with each successive movement 20% shorter than the previous one. After infinitely many such moves, approximately how far in meters will Gita be from her starting point A?

The walk pattern is an infinite spiral: leg $$n$$ has length $$1000 \cdot 0.8^{n-1}$$, directions cycle E, N, W, S.

Net East: $$\dfrac{1000 - 640}{1 - 0.8^4} = \dfrac{360}{0.5904} \approx 609.76$$.

Net North: $$\dfrac{800 - 512}{1 - 0.8^4} = \dfrac{288}{0.5904} \approx 487.81$$.

Distance $$AB = \sqrt{609.76^2 + 487.81^2} \approx \sqrt{609766} \approx \mathbf{781}$$.

Create a FREE account and get:

Download resources