Amedieval city has the shape of a square and is protected by walls with length 500 m and height 15 m. you are the commander of an attacking army and the closest you can get to the wall is 100 m. your plan is to set fire to the city by catapulting heated rocks over the wall (with an initial speed of 80 m/s). at what range of angles should you tell your men to set the catapult?

At 20∘c, the hole in an aluminum ring is 2.800 cm in diameter. you need to slip this ring over a steel shaft that has a room-temperature diameter of 2.804 cm . 1. to what common temperature should the ring and the shaft be heated so that the ring will just fit onto the shaft? coefficients of linear thermal expansion of steel and aluminum are 12×10−6 k−1 and23×10−6 k−1 respectively.