# Calculus 3

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A medieval city has the shape of a square and is protected by walls with length 550 m and height 16 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? (Assume the path of the rocks is perpendicular to the wall. Round the answer to one decimal place. g ≈ 9.8 m/s2)

I have no idea where to start.

• Calculus 3 -

the range R of a projectile fired with angle v at angle θ is

R = v^2 sin(2θ)/g

You have the numbers; solve for θ and you should get two answers. Those will be the minimum and maximum θ which for that range.

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