CHALLENGE - The Princess and the Key
A beautiful princess is locked in a tower.
The lock to the tower can only be opened from the inside.
The princess’ lover has the key but he is outside the tower.
Talking to one another through a window they decide that he should toss the key up to her.
There are windows in the tower. They are trying to decide which window she should lean out and how fast he should throw the key up.
• Use this applet to decide on a combinations of window height and initial speed that will enable the princess to grab the tossed up key. Indicate when and for how long the key is just outside the window.
• What strategy would you advise to maximize the possibility of the key being caught?
• Knowing that the time in seconds for which the height of the key is a maximum is
initialspeed / 9.8 write an expression for the height of the key as a function of time.