A beautiful princess is locked in a tower. [br][br]The lock to the tower can only be opened from the inside. [br][br]The princess’ lover has the key but he is outside the tower.[br][br]Talking to one another through a window they decide that he should toss the key up to her.[br][br]There are many windows along the height of the tower – some are taller windows and some are shorter windows.[br][br]They are trying to decide which window she should lean out and how fast he should throw the key up.[br][br]• Use the Princess and the Key environment to compile a table of at least three possibilities of combinations of [br]window size, window height and initial speed that will enable the princess to grab the tossed up key. [br]For each combination, indicate when and for how long the key is just outside the window.[br][br]• What strategy would you advise to maximize the possibility of the key being caught?[br][br]• Knowing that the time in seconds for which the height of the key is a maximum is [br]initialspeed / 9.8 write an expression for the height of the key as a function of time.