Math Problem Statement

A medieval 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? (Assume the path of the rocks is perpendicular to the wall. Round your answers to one decimal place. Use g ≈ 9.8 m/s2. Enter your answer using interval notation. Enter your answer in terms of degrees without using a degree symbol.)

Solution

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Math Problem Analysis

Mathematical Concepts

Projectile Motion
Trigonometry
Physics of Motion

Formulas

x(t) = v₀ * cos(θ) * t
y(t) = v₀ * sin(θ) * t - (1/2) * g * t²
tan(θ) = y/x
d = v₀ * t * cos(θ)

Theorems

Projectile Motion Equations
Trigonometric Relationships

Suitable Grade Level

Grades 11-12