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A plane P at a constant altitude of 6 km and at a constant speed of 600 km/h A is flying directly away from an observer at O on the ground. The point A on the path of the plane lies directly above O. Let the distance AP be x km, and let the angle of elevation of the plane from the observer be 0. a Show that 0 = tan-'. 600 km/E 6 km -16 de b Show that dt - 3600 radians per hour. %3D x2 + 36 c Hence find, in radians per second, the rate at which 0 is decreasing at the instant when the distance AP is 3 km.

A plane P at a constant altitude of 6 km and at a constant speed of 600 km/h A is flying directly away from an observer at O on the ground. The point A on the path of the plane lies directly above O. Let the distance AP be x km, and let the angle of elevation of the plane from the observer be 0. a Show that 0 = tan-'. 600 km/E 6 km -16 de b Show that dt - 3600 radians per hour. %3D x2 + 36 c Hence find, in radians per second, the rate at which 0 is decreasing at the instant when the distance AP is 3 km.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.2: Trigonometric Equations
Problem 99E
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15 A plane P at a constant altitude of 6 km and at a constant speed of 600 km/h A P is flying directly away from an observer at O on the ground. The point A on the path of the plane lies directly above O. Let the distance AP be x km, and let the angle of elevation of the plane from the observer be 0. a Show that 0 = tan¬1. 600 km/h 6 km do b Show that dt -3600 radians per hour. x² + 36 c Hence find, in radians per second, the rate at which 0 is decreasing at the instant when the distance AP is 3 km.
Transcribed Image Text:15 A plane P at a constant altitude of 6 km and at a constant speed of 600 km/h A P is flying directly away from an observer at O on the ground. The point A on the path of the plane lies directly above O. Let the distance AP be x km, and let the angle of elevation of the plane from the observer be 0. a Show that 0 = tan¬1. 600 km/h 6 km do b Show that dt -3600 radians per hour. x² + 36 c Hence find, in radians per second, the rate at which 0 is decreasing at the instant when the distance AP is 3 km.
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