The Best Way for a Mouse to Escape a Cat, According to Math

For many problems, like a ball falling with air resistance, we can use real physics concepts in each of these tiny steps. The mouse will travel with a constant speed and always move in a direction away from the cat. If I take the cross product of the vector position of the cat and the position of the mouse, I will get a result in the z-direction. I can find the vector from the cat to the mouse and then use that to find a unit vector. But with that unit vector, I can multiply it by the mouse's speed to get a vector velocity.