# Related Rates - Unsure about solution

• carlodelmundo
In summary, the problem involves finding the rate of change, in radians per minute, of the angle of elevation of a missile from a radar station. The missile is rising at a rate of 16,500 feet per minute from a point on the ground 75,000 feet away from the radar station. By using the relation between the missile's height and the angle of elevation, and solving for the rate of change, the answer is 0.175 radians per minute.

## Homework Statement

A Missile rises vertically from a point on the ground 75,000 feet from a radar station. If the missle is rising at the rate of 16,500 feet per minute at the instant when it is 38,000 feet high. What is the rate of change, in radians per minute, of the missile's angle of elevation from the radar station at this instant?

A) 0.175
B) 0.219
C) 0.227
D) 0.469
E) 0.507

## The Attempt at a Solution

Here's my attempted drawing:

http://carlodm.com/calc/PIC.JPG [Broken]

I'm thinking of using cosine... but what good does this do me? I'm so lost. Can I get hints please?

Last edited by a moderator:
You should move your radar station down to ground level, where the missile was launched from. And the angle theta they are talking about is the angle at the radar station. Now write down the relation between Y and theta. It isn't cosine. Now find dY/dt in terms of dtheta/dt.

Thank You Dick.

I've solved the problem. I was a little confused about the satellite station... I overlooked that it could be on the ground! For anyone's use I did the following:

tan [theta] = y / 75,000

sec^2 [theta] d[theta]/dt = (1 / 75,000) dy/dt.

I solved for d[theta]/dt and got a result of .175 radians/min. (I solved for cos^2 [theta] by using the Pythagorean theorem with sides a = 75,000 and b = 38,000)

Thanks Dick!

## What are related rates?

Related rates refer to the concept in calculus where the rate of change of one variable is related to the rate of change of another variable. This is often applied to real-world situations, such as when one variable is changing with respect to time.

## How do I know when to use related rates?

Related rates are used when there is a relationship between two or more changing quantities. This often occurs in real-world scenarios, such as when the sides of a triangle are changing and we need to find the rate of change of the area of the triangle.

## What is the process for solving related rates problems?

The process for solving related rates problems involves identifying the variables and their rates of change, setting up an equation that relates the variables, differentiating both sides of the equation with respect to time, substituting in the known values, and solving for the unknown rate of change.

## What are some common mistakes when solving related rates problems?

Common mistakes when solving related rates problems include not properly identifying the variables and their rates of change, not setting up the correct equation, and not differentiating both sides of the equation correctly. It is also important to always label units and pay attention to the given information.

## How can I check if my solution to a related rates problem is correct?

To check if your solution to a related rates problem is correct, you can plug in the known values and make sure the equation holds true. You can also double check your differentiation and unit conversions. It is always helpful to go through the problem again and make sure all steps were followed correctly.