CS1101C Lab 2 (Even Week)

Ready, Aim, Fire!

The deadline for this lab question is Wednesday 05 October 2005, 23:59:59 hours.

The name of your C program file must be called cannon.c, files with any other name will not be marked.

The Task

A not so clever (you will see why later) cannoneer (someone who fires a cannon) has asked you for help. His job is to fire cannon balls from a cannon sitting on top of a cliff to hit a target on the ground. The cannon balls are fired horizontally and are aimed directly at the target. Assume there is no wind and that air resistance is negligible. This is shown in the diagram below:

As he has no understanding of the underlying physics, he can only blindly follow the "trial and error" method. Starting from a initial launching speed, he observes whether the cannon ball undershoots or overshoots the target. He will then adjust the launching speed by a fixed amount accordingly and tries again. To close in on the target, every time the direction of adjustment changes (i.e. from overshot to undershot or vice versa), he will halve the adjustment amount. This goes on until the cannon ball fells within a reasonable margin from the target or he has tried for 10 times and failed.

As an engineering or science undergrad, you can see a far easier way to do this without going out and launching cannon balls for the whole day. Write a program to show your friend that the result of every launch can be "predicted" precisely.

Your program should read from a data file named "target.txt". Each line of the file contains the following information (you can assume all values to be floating point):

Cliff_Height Target_Distance Initial_Launch_Speed Adjustment Margin

For example:

100.5 50 200 50 10

tells you that the catapult is sitting on top of a cliff of 100.5 meters. The target is 50 meters from the cliff. The launching practice should starts with a initial launch speed of 200 meters/second, and adjusted with 50 meters/second until the cannon ball fells not more than 10 meters from the target.

As you should realize by now, this is simply to calculate the horizontal projectile movement (or parabolic movement). The two related formula are given below:

    Vertical Distance = 0.5 * g * t^2
    Horizontal Distance = LaunchSpeed * t

where, g is the gravity (taken as 10 m/s^-2), t is the flight time of the cannon ball, and Vertical Distance is the height of the cliff.

After the every launch, you should adjust the launch speed accordingly (increase if undershot, decrease if overshot) by the Adjustment amount. As mentioned earlier, whenever you encounter a change in adjustment direction, this Adjustment amount would be halved. Finally, whenever the cannon ball falls within the acceptable margin or you have tried for 10 times, the practice terminates.

Additional information:

The input file contains only positive floating point value, i.e. there is no need to check for invalid input.
Your program will read in a single line (a single setting) and executes until either of the ending conditions are met. The program should then proceed to the next line in the input file. Each line represents one experimental setup. The whole execution should terminate when you reach the end of the input file.
You have to make sure that the adjusted launching speed does not drop below 0m/s, else the cannon will fire backwards and kill the cannoneer (which isn't a particularly smart thing to do). It is acceptable to have a launching speed of exactly 0m/s, but a negative launching speed is not allowed. If the launching speed is negative, set it to 0m/s.

Hint 1: Think carefully on how to model the "direction of adjustment". A correct modelling can simplify your program significantly.

Hint 2: Don't forget the math Library functions sqrt() and fabs()......

Sample Run

Below is the sample data file "target.txt" used:

100.5 50 200 50 10
100.5 1000 200 50 5
100.5 1000 200 50 .5

Below is the output your program should produce. Observe the changes of the adjustment amount whenever the direction changes. Note that comments (indicated by "//") are included to explain the output. Your program should not contain these comments in the output.

Sample Output:

Catapult at cliff of 100.50m                    //First setting
Target at 50.00m from cliff
Acceptable margin 10.00m
Shooting Starts:
    Launch speed of 200.00 m/s hit distance of 896.66m
        Launch speed adjusted to 150.00 m/s

    Launch speed of 150.00 m/s hit distance of 672.50m
        Launch speed adjusted to 100.00 m/s

    Launch speed of 100.00 m/s hit distance of 448.33m
        Launch speed adjusted to 50.00 m/s

    Launch speed of 50.00 m/s hit distance of 224.17m
        Launch speed adjusted to 0.00 m/s

    Launch speed of 0.00 m/s hit distance of 0.00m
        Launch speed adjusted to 25.00 m/s              //direction change

    Launch speed of 25.00 m/s hit distance of 112.08m
        Launch speed adjusted to 12.50 m/s              //direction change

    Launch speed of 12.50 m/s hit distance of 56.04m
        Mission accomplished                            //within margin

Catapult at cliff of 100.50m                            //Second Setting
Target at 1000.00m from cliff
Acceptable margin 5.00m
Shooting Starts:
    Launch speed of 200.00 m/s hit distance of 896.66m
        Launch speed adjusted to 250.00 m/s

    Launch speed of 250.00 m/s hit distance of 1120.83m
        Launch speed adjusted to 225.00 m/s         //direction change

    Launch speed of 225.00 m/s hit distance of 1008.74m
        Launch speed adjusted to 200.00 m/s

    Launch speed of 200.00 m/s hit distance of 896.66m
        Launch speed adjusted to 212.50 m/s         //direction change

    Launch speed of 212.50 m/s hit distance of 952.70m
        Launch speed adjusted to 225.00 m/s

    Launch speed of 225.00 m/s hit distance of 1008.74m
        Launch speed adjusted to 218.75 m/s         //direction change

    Launch speed of 218.75 m/s hit distance of 980.72m
        Launch speed adjusted to 221.88 m/s         //direction change

    Launch speed of 221.88 m/s hit distance of 994.73m
        Launch speed adjusted to 225.00 m/s

    Launch speed of 225.00 m/s hit distance of 1008.74m
        Launch speed adjusted to 223.44 m/s         //direction change

    Launch speed of 223.44 m/s hit distance of 1001.74m
        Mission accomplished                       //within margin

Catapult at cliff of 100.50m                        //Third Setting
Target at 1000.00m from cliff
Acceptable margin 0.50m
Shooting Starts:
    Launch speed of 200.00 m/s hit distance of 896.66m
        Launch speed adjusted to 250.00 m/s

    Launch speed of 250.00 m/s hit distance of 1120.83m
        Launch speed adjusted to 225.00 m/s

    Launch speed of 225.00 m/s hit distance of 1008.74m
        Launch speed adjusted to 200.00 m/s

    Launch speed of 200.00 m/s hit distance of 896.66m
        Launch speed adjusted to 212.50 m/s             //direction change

    Launch speed of 212.50 m/s hit distance of 952.70m
        Launch speed adjusted to 225.00 m/s

    Launch speed of 225.00 m/s hit distance of 1008.74m
        Launch speed adjusted to 218.75 m/s             //direction change

    Launch speed of 218.75 m/s hit distance of 980.72m
        Launch speed adjusted to 221.88 m/s             //direction change

    Launch speed of 221.88 m/s hit distance of 994.73m
        Launch speed adjusted to 225.00 m/s

    Launch speed of 225.00 m/s hit distance of 1008.74m
        Launch speed adjusted to 223.44 m/s             //direction change

    Launch speed of 223.44 m/s hit distance of 1001.74m
        Launch speed adjusted to 221.88 m/s             //10th try.

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