CMSI 186 - Problem Set #1

CMSI 186 Problem Set #1 Discrete Simulation Due Thursday, January 29

Overview

In this assignment you will program discrete simulations of a couple of physical systems, in order to answer some questions about their behavior.

In both problems there are some natural opportunities for using Java objects: in the Clock Problem, for example, you will probably want to define a class of Clock objects, with methods like void tick() and int hour(); in the Playground Problem, Ball objects seem appropriate, with methods like void move() and boolean isTouching(Ball), etc. You must write unit tests for your classes before you begin coding the methods.

The Clock Problem

Make a program that determines all of the times during a twelve-hour day at which a clock's hands form a straight line. The program should perform a discrete simulation of a clock, using the basic approach and program structures that were discussed in class.

You should test your program on all sorts of inputs. What happens as the grain gets very small (e.g., 0.0001)? (Apart from the increased running time of the program) do you notice anything funny about the outputs? Give an explanation for this behavior.

The Playground Problem

On a large, flat playground, with a narrow flagpole in the center, we have placed four playground balls, each with a radius of exactly one foot. They are kicked, simultaneously, in different directions and at different speeds. The problem is to determine, by a discrete simulation of the physical situation, whether any ball will collide with any other ball or with the flagpole, and, if so, when and where the first such collision will take place. You may assume that the balls travel in a straight line and maintain a constant speed until collision.

We can model the situation by imagining a coordinate system on the playground where (0.0,0.0) is the exact center of the playground, and (x,y) is exactly x feet east and y feet south of the center (for reasons that will become clear later).

The starting position of each ball will be specified by giving the coordinates (x,y) of its center.

The speed at which a ball is kicked can also be given by a pair of numbers (dx,dy), where dx gives the number of feet per second that the ball is moving in the +x (easterly) direction, and dy gives the number of feet per second that the ball is moving in the +y (northerly) direction.

Thus, any particular instance of the problem is specified by giving seventeen numbers, namely, the grain of time for which the simulation should be carried out, and, for each of the four balls, the values x, y, dx, and dy.

Make program PlaygroundSolver which will be invoked with sixteen or seventeen arguments, all doubles, as follows:
```
    java PlaygroundSolver x0 y0 dx0 dy0 x1 y1 dx1 dy1 x2 y2 dx2 dy2 x3 y3 dx3 dy3 grain_optional
```

The program should output a system status report every simulated minute, plus a final report indicating when and where the first collision will occur (or a message indicating that no such collision will ever take place). The final argument is optional; if specified, it defines the size of the grain in seconds, and is required to be in the range
```
   0.0 < grain <= 60.0 ;
```
if absent, use a default grain of one second.

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Revised: January 29, 2009