Math Problem Statement
An arrow is shot at an angle of θ=45∘ above the horizontal. The arrow hits a tree a horizontal distance D=220m away, at the same height above the ground as it was shot. Use g=9.8m/s2 for the magnitude of the acceleration due to gravity.Find ta , the time that the arrow spends in the air. Answer numerically in seconds, to two significant figures.
Solution
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Math Problem Analysis
Mathematical Concepts
Projectile Motion
Kinematics
Formulas
Horizontal Range: D = v₀ * ta * cos(θ)
Time of Flight: ta = (2 * v₀ * sin(θ)) / g
Relationship: ta² = (2 * D * sin(θ) * cos(θ)) / g
Simplified: ta² = 2D/g
Theorems
Trigonometric Identity: sin(2θ) = 2sin(θ)cos(θ)
Suitable Grade Level
Grades 11-12
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