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A graphing calculator is recommended. A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.22. It can be shown that the downward velocity of the sky diver at time t is given by v(t) = 150(1e-0.22t) where t is measured in seconds (s) and v(t) is measured in feet per second (ft/s). (a) Find the initial velocity of the sky diver. ft/s (b) Find the velocity after 5 s and after 10 s. (Round your answers to one decimal place.) after 5 s ft/s ft/s after 10 s (c) Draw a graph of the velocity function v(t).

A graphing calculator is recommended. A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.22. It can be shown that the downward velocity of the sky diver at time t is given by v(t) = 150(1e-0.22t) where t is measured in seconds (s) and v(t) is measured in feet per second (ft/s). (a) Find the initial velocity of the sky diver. ft/s (b) Find the velocity after 5 s and after 10 s. (Round your answers to one decimal place.) after 5 s ft/s ft/s after 10 s (c) Draw a graph of the velocity function v(t).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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A graphing calculator is recommended. A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.22. It can be shown that the downward velocity of the sky diver at time t is given by v(t) = 150(1e-0.22t) where t is measured in seconds (s) and v(t) is measured in feet per second (ft/s). (a) Find the initial velocity of the sky diver. ft/s (b) Find the velocity after 5 s and after 10 s. (Round your answers to one decimal place.) after 5 s ft/s ft/s after 10 s (c) Draw a graph of the velocity function v(t). v(t) 200 150 100 50 v(t) 200 150 100 50 10 10 20 20 30 30 40 t 40 v(t) 200 150 100 50 10 20 10 v(t) 200 150 L 100 50 30 20 30 (d) The maximum velocity of a falling object with wind resistance is called its terminal velocity. From the graph in part (c) find the terminal velocity of this sky diver. (Round your answer to the nearest whole number.) ft/s
Transcribed Image Text:A graphing calculator is recommended. A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.22. It can be shown that the downward velocity of the sky diver at time t is given by v(t) = 150(1e-0.22t) where t is measured in seconds (s) and v(t) is measured in feet per second (ft/s). (a) Find the initial velocity of the sky diver. ft/s (b) Find the velocity after 5 s and after 10 s. (Round your answers to one decimal place.) after 5 s ft/s ft/s after 10 s (c) Draw a graph of the velocity function v(t). v(t) 200 150 100 50 v(t) 200 150 100 50 10 10 20 20 30 30 40 t 40 v(t) 200 150 100 50 10 20 10 v(t) 200 150 L 100 50 30 20 30 (d) The maximum velocity of a falling object with wind resistance is called its terminal velocity. From the graph in part (c) find the terminal velocity of this sky diver. (Round your answer to the nearest whole number.) ft/s
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