Math Problem Statement
A projectile is launched from a cliff of height H. It is launched with an initial velocity v0 and angle 𝞱 above the horizontal. Answer the following in terms of given quantities (in bold) and fundamental constants (“g”).
What is its hangtime?
What is its horizontal range?
When will it be descending at a 45 degree angle?
Solution
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Math Problem Analysis
Mathematical Concepts
Projectile Motion
Kinematics
Quadratic Equations
Trigonometry
Formulas
y(t) = H + v_0 sin(𝞱) t - (1/2) g t^2
Quadratic formula for time: t = [v_0 sin(𝞱) ± sqrt((v_0 sin(𝞱))^2 + 2 g H)] / g
Horizontal range: R = v_0 cos(𝞱) × t
Time when descending at 45 degrees: t = v_0 (sin(𝞱) + cos(𝞱)) / g
Theorems
Quadratic formula
Suitable Grade Level
Grades 11-12 (Advanced High School Physics)
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