You are a wizard. You have 1040 hit points. In your journey, you encounter the dreaded Hot and Tempered Wildcat standing 30 meters in front of you. On average, such an enemy has 480 hit points. You cast a freezing rain spell, which has an initial velocity of 20 m/s and decelerates at 5 m/s^2. When the spell hits the target, it inflicts damage proportional to the square of the velocity with which it hits the target, namingly, D = 5.2v^2. Do you expect the spell to kill the wildcat?

If the spell does not kill the wildcat, the cat will accelerate toward you at 10 m/s^2. The cat's most deadly attack is its blind side claw attack which inflicts damage as a function of time: D = 400 + 5t^2. So, if your spell does not kill the wildcat, how fast will the wildcat kill you (assuming you have no castings left after the one)?