It's Christmas Eve and Santa Claus has taken off from North Pole with his sleigh full of presents to distribute them to the all the kids around the globe. Unfortunately, the Grinch, who hates holidays and wants to destroy and steal Christmas, has set a mean plan to take Santa down. He is using a cannon, which is placed in Iceland and is targeted towards Santa's sleigh. He wants to shoot the sleigh and bring down all the presents for himself!

Assume you are the Grinch. Listening to the news, you heard that Santa's sleigh was reported to be at the following coordinates during his journey:

Develop a MATLAB program to calculate the trajectory of both the Santa Claus and the cannon ball and make sure that the cannon ball hits Santa and releases all the presents. In order to calculate the sleigh's trajectory you will need to use the coordinates given in Table 1 and use a curve-fitting algorithm to extract the trajectory's equation. Your program should have all the necessary values for the initial velocity of both objects (Santa's sleigh and cannon ball), the launch angle from horizontal line and the gravitational acceleration. In order the cannon ball to hit the sleigh, you will need to calculate the intersection point of the two trajectories. After the calculation, an animation of the trajectories should be produced, by modelling all the objects involved (i.e. the sleigh, the ball etc.). Finally, after the collision of the two objects, you need to re-calculate the new direction of the sleigh's velocity (assume that its value remains constant and the same as the initial velocity, for simplicity) and determine the point where the sleigh will hit the ground. Do not forget to add appropriate comments to your code and use reasonable names for your variables. Notes:

1. The velocities of the objects are constant.

2. The air resistance is negligible.

3. The alteration of the gravitational acceleration is not taken into account.

4. The mass of the sleigh and the cannon ball are respectively: m _sleigh = 200 kg, m _ball , = 15 kg

5. The (0,0) point is located on the cannon.

X coordinate 10.80 19.40 23.00 27.80 Y coordinate 16.16599 25.4055 28.31672 31.32027 34.42243 34.43723 34.4029 34.33013 38.90 39.50 41.05 42.00 Table 1. Santa's sleigh x and y coordinates