3

2. (10 points) Diesel tends to wait until the rabbit is closest before starting to chase. If the rabbit

is traveling across the yard in a straight line, we can assume the simulation will start when the

rabbit is located at [x (0), y (0)] = [x , 0] and have a velocity of [x (0), y (0)] = [0, C ], where RR0 RRR

CR is the maximum speed at which the rabbit can run. Note, we are ignoring acceleration here, we are just assuming the rabbit has already accelerated to it's max velocity and stays there. So, the velocity vector can change direction, but not magnitude. And the rabbit will change direction, so the velocity will change direction. From my observation, it does so when Diesel gets within a certain distance of the rabbit. But to keep it simple, suppose the rabbit just turns 90 degrees to the right at a fix rate of 90 degrees/second starting at t = 2.

Write the equations for the rabbit's velocity, i.e. x R(t) and y R (t).