Chapter 4 Appl Introduction A rocket is being launched from the ground and camer

Question

Chapter 4 Appl Introduction A rocket is being launched from the ground and cameras are recording the event. A video camera is loc a certain the launch pad. At what rate should the angle off inclination (the angle the cam ground) distance from the camera to record the flight of the rocket as it heads upward? (See Example change to allow rocket launch involves two related quantities that change over time. Being able to solve this type one derivatives introduced in this chapter. We also look at how derivatives are used to application of minimum values of functions. As a result, we will be able to solve applied optimization problems, s revenue and minimizing surface a In addition, we examine how derivatives are used to evaluate co approximate roots of functions, and to provide accurate graphs of functions. 4.1 l Related Rates Learning Objectives 4.1.1 Express changing quantities in terms of derivatives 4.1.2 Find relationships among the derivatives in a given problem. depends on 4.1.3 Use the chain rule to find the rate of change of one quantity that change of other quantities. We have seen that for quantities that are changing over time, the rates at which these quantities derivatives. If two related quantities are changing over time, the rates at which the quantities ch example, if a balloon is being filled with air, both the radius of the balloon and the volume of the b In this section, we consider several problems in which two or more related quantities are changing determine the relationship between the rates of change of these quantities. Setting up Related-Rates Problems In many real-world applications, related quantities are changing with respect to time. For examp balloon example again, we can say that the rate of in the volume, is to the r. In this case, we say that dV and dr are related rates because Vis related to r. Here we stud dt dt related quantities that are changing with respect to time and we look at how to calculate one rate o rate of change.

Explanation / Answer

let A's distance =x, and B's distance =y

hence total distance d2 =x2+y2

differentiating above with respect to t

2d*(dd/dt) =2xdx/dt+2ydy/dt

50*(dd/dt) =30*(-250)+40*(-300)

(dd/dt)=-390 miles/hour

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