Suppose that there is a plane flying over the earth, equipped with a cannon that is pointed towards the earth. the cannon shoots a 2kg cannonball at earth at an initial speed of 300 ft/s. but this is no ordinary cannonball. this is a smart cannonballtm. after being fired it will gradually reconfigure its shape to be- come more aerodynamic to reduce air resistance. following the convention that forces acting on the cannonball in the direction away from earth are neg ative, the smart corporation estimates that after t seconds of being fired the force from air resistance exerted on the cannonball will be- where v is the velocity of the cannonball at time t using this new estimate for the force of air resistance on the cannonball, write down a differential equation that models the motion of the cannonball. then find a function v(t) that returns the velocity of the cannonball after t seconds of being fired. for you solution v(t) in question 4, calculate the limit lim v(t). does the differ ential equation you developed in the previous question have any equilibrium solutions? based on this information, what can you conclude about the accu- racy of smart corporation's claim that the force from air resistance will be given by after t seconds? t-oo + u