1. A ball is thrown from the top of a roof at an angle of 20o with respect to the vertical. 1 s later a ball is dropped from the top of the roof.
a) If the height of the roof is 20 m, determine the velocity with which the first ball must be thrown in order for both balls to land at exactly the same time.
b) Imagine the velocity of the first ball is now known, and instead it is the height of the building which is unknown. Can you obtain an equation for the height of the building which would result in both balls landing on the floor at the same time.
2. You are firing a cannonball from the top of a cliff at a pirate ship which is behind a mountain. The height of the cannon is 100 m, the height of the mountain is 120 m, and the height of the pirate ship is 70 m.
The mountain is horizontally 200 m away from cannon, while the pirate ship is horizontally 270 m away from the cannon.
The speed of the cannonball after it is fired is 65 m s-1. You could hit anywhere from the bottom of the pirate ship to the top in order to sink it. Over what angles could you fire the cannonball to sink the pirate ship?