Question

QUESTION 26/27 To enter a port, a ship must navigate between the shore and the tip of a jetty. You must instruct the captain to take a trajectory such that the ship is always equally as far from the tip of the jetty A-(0,a) as from the closest point S on the shore y -0, as shown in the Figure. jetty a A - (0,a) shore (a) (2 marks) Let P - (x, y) be the position of the ship on its trajectory. Draw qualitatively the (b) (2 marks) Determine the distance between the boat and the tip of the jetty, and the distance (c) (2 marks) Using the results from the previous point and the constraint that these distances ship's trajectory between the boat and the shore as a function of the boat's location P-(x.y) be equal, show that the trajectory that the ship must follow is given by xa 2a 2 (d) (2 marks) Find the unit tangent vector f(x) to the boat's trajectory, corresponding to the heading of the ship, as a function of x (e) (2 marks) The captain is unable to measure precisely how far away the boat is from the shore. To help the captain navigate, determine the angle β(x) between the ship's heading (10 marks)

Answer 1

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