A two dimensional skier must slalom down a slope, by going through n parallel gates of known position (x i , y i ), and of width c i , i 1, , n The initial position (x 0 , y 0 ) is given, as well as the final one, (x n 1 , y n 1 ) Here, the x axis represents the direction down the slope, from left ...

1 Assume that x i z i is the crossing point of gate i the pa ...

A two-dimensional skier must slalom down a slope, by going through n parallel gates of known position

Question:

A two-dimensional skier must slalom down a slope, by going through n parallel gates of known position (x_i, y_i), and of width c_i, i = 1, . . . , n. The initial position (x₀, y₀) is given, as well as the final one, (x_n+1, y_n+1). Here, the x-axis represents the direction down the slope, from left to right.

1. Find the path that minimizes the total length of the path. Your answer should come in the form of an optimization problem.
2. Try solving the problem numerically, with the data given in Table 9.3.

In Table 9.3.