Aim of the Game
The aim of this game is to get the ball in the hole, creating gliders for the ball. You can do this
by clicking on the gamefield. Depending on the slope of the glider, the ball will have a certain acceleration. A high
slope will give a high acceleration. If the ball is too slow when it reaches the hole, it won't be able to push
through the seal. But if the ball is too fast it will bounce out of the hole again. The correct speed will be between
85 and 90. The maximum number of gliders you
can use is six. And when the ball hits one of the four walls of the room, you are game over.
Maths -- Dot Product of Two Vectors
This applet explains the dot product of two vectors. To calculate the acceleration of the ball we need to know
the angle between the vector representing the glider (A) and the horizontal vector (B), where
A is the glider (x,y) and
B is always
equal to (1,0). To calculate this angle we use the following formula:
Where
is the dot product between the two vectors A and B.
The dot product between two vectors (a,b) and (c,d) is equal to ac + bd, so
therefore the dot product between A and B is equal to 1x + 0y = x
is the length of vector A, which is . And, using the same formula,
we find that the length of
vector B is equal to 1.
If you select the 'Get Explanation' option and then click on a line, the calculated values for this line will appear
in the top right corner.
. And, using the same formula,
we find that the length of
vector B is equal to 1.