You are a Middle Ages cannonball scientist attacking a castle a distance D away. Your job is to get a cannonball of mass m over the walls, which are a height H above the top of the cannonball launcher. At the instant when the cannonball leaves the launcher it will be traveling at a speed v0 directed at an angle ¦È above the horizontal.
1. Write the cannonball¡¯s coordinates x(t) and y(t) in terms of v0, ¦È, m, and g, or a subset of these quantities. Define your x-y coordinate system as shown in the figure with the origin at the end of the cannonball launcher, and set the time to t = 0 at the instant when the cannonball leaves the launcher.
2. At what time tD, does the x-coordinate of the cannonball reach the x-coordinate of the wall?
3. What is the value of the y-coordinate of the cannonball at the instant when the x-coordinate reaches the castle wall?
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