1. Related Rates Problems

2. A hot-air balloon rising straight up from a level field is tracked down by a television camera located 500 ft away from the lift-off position. At the moment the camera’s angle of elevation is π/4, the angle is increasing at the rate of 0.14 rad/min. How fast is the balloon rising at that moment? 1.Draw a picture and name the variables and constants. Camera Balloon 500 ft y θ 2.Write down the numerical information you were given. At some time, θ = π/4 3.Write down what you are asked to find.4.Write an equation that relates the variables.5.Differentiate with respect to t.6.Evaluate.

3. A police cruiser, approaching a right angled intersection from the north, is chasing a speeding car that has turned the corner and is now moving straight east. When the cruiser is 0.6 mi north of the intersection and the car is is 0.8 mi to the east, the police determine with radar that the distance between them and the car is increasing at 20 mph. If the cruiser is moving at 60 mph at the instant of the measurement, what is the speed of the car? 1.Draw a picture and name the variables and constants. Car Police cruiser x z y 2.Write down the numerical information you were given. At some time, x = 0.8 mi and y = 0.6 mi 3.Write down what you are asked to find.4.Write an equation that relates the variables.5.Differentiate with respect to t.6.Evaluate. …so z = 1 mi

4. Water is running out of a conical funnel at the rate of 1 cubic in per second. The radius of the base of the funnel is 4 in and its altitude is 10 in. Find the rate at which the water level is dropping when the water level is 6 in from the top of the funnel. 1.Draw a picture and name the variables and constants.2.Write down the numerical information you were given. At some time, h = 4 in 3.Write down what you are asked to find.4.Write an equation that relates the variables.5.Differentiate with respect to t.6.Evaluate. Using similar triangles:

5. is constant… is not constant… Why?