h = overall velocity of the ball (the hypotenuse)x = x component of the ball velocity
y = y component of the ball velocity
0 = theta, angle of the path of the ball, set to a randomly generated number between 35o and 55o
x = sin 0 * h
y = cos 0 * h
Trigonometry:
Trigonometry can be used to calculate angles. In right-angled triangles, where there is a hypotenuse, the term SOHCAHTOA can be used:
- SOH = sine = opposite/hypotenuse
- CAH = cosine = adjacent/hypotenuse
- TOA = tan = opposite/adjacent
Pythagoras theorem:
In a right-angled triangle, the hypotenuse is equal to the sum of the other two sides. Often written as: a2+b2=c2
Random number generation:
For the ball to leave the paddle at the start of each game using a different angle, a random number between two set boundary numbers should be generated and control the ball’s initial movement. The boundary numbers are 35o and 55o as these were considered suitable angles between which to project the ball from the paddle.
To create a random number between these boundaries the srand code is implemented to initialise the random number generator, using processor clicks, as these values are different every time the program runs. The boundary angles are then set and the angle must be between these values, it is then multiplied by 2pi/360, and converted to radians. The ball velocity in x and y are then calculated and the remainder of the random number is divided by 2, giving an answer of 0 or 1, allowing the x component to be reversed, changing to direction the ball takes as it leaves the paddle.