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# Derivatives : Trigonometry Rate of Change Problems

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1.) A fugitive is running along a wall at 4.0m/s. A searchlight 20m from the wall is trained on him. How fast is the searchlight rotating at the instant when he is 10m from the point on the wall nearest the searching?

2.) A balloon is rising from the ground at the rate of 6.0m/s from a point 100m from an observer, also on the ground. Use inverse trigonometric functions to determine how fast the angle of inclination of the observer's line of sight is increasing when the balloon is at altitude of 150m.

3.) A man is walking toward a building 80.0m high at the rate of 1.5 m/s. How fast is the angle of elevation of the top increasing when he is 40.0m away from the building?

4.) A hallway is 2m wide and runs perpendicularly into another hallway 5m wide. What is the length of the longest think pole that can be moved horizontally around the corner?

5.)A gutter is to be made from a long piece of metal 24cm wide by turning up strips 8cm wide along each side such a way that they make equal angles (Theta) with the vertical.For what value of (Theta) will the cross sectional area be the greatest?