6. A medieval city has the shape of a square and is protected by walls of...

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6. A medieval city has the shape of a square and is protected by walls of length 500m and height 15m (assume zero width). You are the commander of an attacking army and the closest you can get to the wall is 100m. Your plan is to set fire to the city by catapulting flaming rocks over the wall (with an initial speed of 80m/s). By following the parts below, we want to know what range of angles, in degrees, you should order your troops to set the catapult? (Assume the path of the rocks is perpendicular to the wall, the ground is level with walls and you only want to hit inside the city (not the back walls)). Take the acceleration due to gravity to be 9.8 m/s. 1 (a) Using the formula xmax = v sin (20) from lectures, set up two inequalities on sin(20) that express the fact that the projectile lands inside the city. (b) Find another inequality on g that expresses that the projectile should go over the nearest wall (you do not need to explicitly solve it for 0; it can and will have expressions like tan and cos 0 in it). (c) Use a calculator/computer to solve these inequalities and hence find numerical ranges for . You can ask Wolfram Alpha to do this as follows: if you have two conditions A (say from part (a)) and B (from part (b)) with parameter range C, you can input it into Wolfram Alpha the following way: N({A,B,C}) Here, N(x) returns a numerical value for the input x (solution to our problem). Then convert your ranges to degrees by multiplying by 180 T 6. A medieval city has the shape of a square and is protected by walls of length 500m and height 15m (assume zero width). You are the commander of an attacking army and the closest you can get to the wall is 100m. Your plan is to set fire to the city by catapulting flaming rocks over the wall (with an initial speed of 80m/s). By following the parts below, we want to know what range of angles, in degrees, you should order your troops to set the catapult? (Assume the path of the rocks is perpendicular to the wall, the ground is level with walls and you only want to hit inside the city (not the back walls)). Take the acceleration due to gravity to be 9.8 m/s. 1 (a) Using the formula xmax = v sin (20) from lectures, set up two inequalities on sin(20) that express the fact that the projectile lands inside the city. (b) Find another inequality on g that expresses that the projectile should go over the nearest wall (you do not need to explicitly solve it for 0; it can and will have expressions like tan and cos 0 in it). (c) Use a calculator/computer to solve these inequalities and hence find numerical ranges for . You can ask Wolfram Alpha to do this as follows: if you have two conditions A (say from part (a)) and B (from part (b)) with parameter range C, you can input it into Wolfram Alpha the following way: N({A,B,C}) Here, N(x) returns a numerical value for the input x (solution to our problem). Then convert your ranges to degrees by multiplying by 180 T