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Elevator An observer is 22 m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 16 m horizontally from the observer (see figure). The angle of elevation of the elevator is the angle that the observer's line of sight makes with the horizontal (it may be positive or negative). Assuming that the elevator rises at a rate of 2 m/s, what is the rate of change of the angle of elevation when the elevator is 14 m above the ground? When the elevator is 38 m above the ground? Observer 22 m 16 m Write an equation relating the angle, 0, and the vertical distance between the height of the elevator and the height of the observer, H. Differentiate both sides of the equation with respect to t. HP dt d0 dt When the elevator is 14 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) When the elevator is 38 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) rad/s rad

Elevator An observer is 22 m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 16 m horizontally from the observer (see figure). The angle of elevation of the elevator is the angle that the observer's line of sight makes with the horizontal (it may be positive or negative). Assuming that the elevator rises at a rate of 2 m/s, what is the rate of change of the angle of elevation when the elevator is 14 m above the ground? When the elevator is 38 m above the ground? Observer 22 m 16 m Write an equation relating the angle, 0, and the vertical distance between the height of the elevator and the height of the observer, H. Differentiate both sides of the equation with respect to t. HP dt d0 dt When the elevator is 14 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) When the elevator is 38 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) rad/s rad

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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Elevator An observer is 22 m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 16 m horizontally from the observer (see figure). The angle of elevation of the elevator is the angle that the observer's line of sight makes with the horizontal (it may be positive or negative). Assuming that the elevator rises at a rate of 2 m/s, what is the rate of change of the angle of elevation when the elevator is 14 m above the ground? When the elevator is 38 m above the ground? 0>0 0<0 Observer 22 m 16 m Write an equation relating the angle, 0, and the vertical distance between the height of the elevator and the height of the observer, H. Differentiate both sides of the equation with respect to t. d0 HP %3D dt dt When the elevator is 14 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) When the elevator is 38 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) rad/s rad m/s
Transcribed Image Text:Elevator An observer is 22 m above the ground floor of a large hotel atrium looking at a glass-enclosed elevator shaft that is 16 m horizontally from the observer (see figure). The angle of elevation of the elevator is the angle that the observer's line of sight makes with the horizontal (it may be positive or negative). Assuming that the elevator rises at a rate of 2 m/s, what is the rate of change of the angle of elevation when the elevator is 14 m above the ground? When the elevator is 38 m above the ground? 0>0 0<0 Observer 22 m 16 m Write an equation relating the angle, 0, and the vertical distance between the height of the elevator and the height of the observer, H. Differentiate both sides of the equation with respect to t. d0 HP %3D dt dt When the elevator is 14 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) When the elevator is 38 m above the ground, the rate of change of the angle of elevation is (Type an exact answer in simplified form.) rad/s rad m/s
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