1. Suppose that in Sherwood Forest, the average radius of a tree is R = 1 m and

Question

1. Suppose that in Sherwood Forest, the average radius of a tree is R = 1 m and the average number of trees per unit area is ? = 0.005 m?2. If Robin Hood shoots an arrow in a random direction, how far, on average, will it travel before it strikes a tree?

(a) Find the solution theoretically on paper, listing all the steps and assumptions.

(b) Verify your answer with Monte Carlo computer code. Use any language that you like. Make sure that you shoot enough arrows in enough forests. Turn in the code electronically.

Explanation / Answer

Answer:-

a) & b)

If the trees are uniformly distributed, total portion of the circular boundary covered

= (0.005 * L * L * Pi * 2 m) / (2 * Pi * L m)

= 0.005 * L

Thus, the average distance covered so that the arrow hits at least 1 tree is L when :

1 = 0.005 * L

So, L = 1 / (0.005) m = 200 m.

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