Math Problem Statement
A skydiver's height above ground is h(t) = 10850 − 170t − 850e−0.2t where h is in feet and t is in seconds. At what instant in time is she falling at 120 feet per second? Be accurate to two decimal places and include correct units.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Exponential Functions
Formulas
Velocity: v(t) = dh/dt
Derivative of an exponential: d/dt[e^(-kt)] = -ke^(-kt)
Natural logarithm for solving equations: ln(x)
Theorems
Derivative as the rate of change
Exponential decay
Suitable Grade Level
Grades 11-12, College Calculus
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