Objective:
The students will develop strategies and use vector component skills.
In the Film:
Racing strategy is dictated by a drivers experience and by the field of competition. When the race is on, you try to follow your game plan. However, you cannot predict the moves of your opponents, nor a host of other factors. You will need contingency plans, and you must be prepared to implement them.
Background:
Velocity can be thought of as having two independent components, namely, forward or backward and left or right. In this game the students must control movement in both directions: forward or backward, left or right.
Materials:
Graph paper and pencil.
To Set Up:
Following the illustration, draw the outline or walls of a raceway on a few pieces of graph paper. Mark a start line and a finish line for each raceway. Divide the class into groups of three or four. Give each group an outline of the raceway. The students may design their own racetracks in later games. Have them learn and follow the rules below.
The Start:
Choose the order of play (who goes first). Each car picks a position on the start line, beginning with the first player. Cars are always placed at the intersection of graph paper grid lines. Cars begin with a velocity of (0,0), that is, zero squares forward and zero squares to the side.
To Move:
Each car in turn may choose to change velocity in either of the directions or not. The velocity may change forward or backward by only one unit. The velocity may also change left or right by only one unit. The new velocity (forward or backward and left or right) must be recorded (see example in figure 1) and then plotted out on the graph paper (see example in figure 2). Note that a component must go to zero before it can change direction. If a car lands outside the raceway or if any point along the path of the car touches a wall, that car has crashed and is out of the race. A car may not land on a position already occupied by another car. The driver must change velocity to avoid a collision with another car, even if it means crashing into a wall.
To Win:
The first car to reach the finish line, regardless of starting position, wins.
Whats Going On?
The students have to keep track of their velocities in both directions and make decisions based on their speed and the changing shape of the track. What they record in brackets (see example in figure 1) is the cars velocity at a given point in time. What they plot on the track (graph paper) is the cars new position caused by that velocity. The maximum one-unit change in velocity is the allowable acceleration (or deceleration) of the car. The best way to play the game is very close to the way real drivers must learn to make turns. The game also illustrates the need to slow for turns.
Taking It Further:
1. Different turn shapes and narrows determine the degree of complexity of a raceway. The students can design different raceways to vary the games difficulty.
2. The rules may be varied. For example, speeding up and/or slowing down can change by two or three units instead of just one.
