Develop a simulation of a 2D ball bouncing off of a slanted floor as shown below.

For this simulation we assume the following:

• The ball is initially released from height \(h=100\)
• The coefficient of friction for the ball is \(\gamma = 0.0001\)
• The acceleration due to gravity is \(9.8\ m/s^2\)
• The floor is slanted at \(10\) degrees
• The ball is initially at rest

Bonus

• Can you simulate more than one ball? Each ball will be released at a different height and hit the floor at a different location

Technical notes

Computing the angle of reflection off of a slanted floor

Consider the figure shown below figure. \(\mathbf{i}\) represents the incoming direction. \(\mathbf{o}\) represents the outgoing direction. \(\mathbf{n}\) is the surface normal.

Notice that \[ 2 \mathbf{n} (\mathbf{i} . \mathbf{n}) = \mathbf{i} + \mathbf{o} \] Therefore, \[ \mathbf{o} = 2 \mathbf{n} (\mathbf{i} . \mathbf{n}) - \mathbf{i} \]

Submission

The exercise will be completed in class, and you do not need to submit anything. Be prepared to show your work to the instructor.

You can find starter code here.