# Baseball Diamond Distance Problem

• zelphics
In summary, a baseball diamond is a square with sides 90 feet long. A player is running from first base to second base at a rate of 16 ft/sec. Using the derivative, the player's rate of change of distance from third base can be found by differentiating the equation a^2+b^2=C^2 and plugging in the given values. The resulting equation is da/dt(2a) + db/dt(2b) = dc/dt(2c).
zelphics

## Homework Statement

A baseball diamond is a square 90 feet on a side. A player runs from first base to second at a rate of 16 ft/sec. At what rate is the player's distance from third base changing when the player is 30 ft from first base..

## Homework Equations

dr/dt ds/dt

dx/dt? a^2+b^2=C^2

## The Attempt at a Solution

I have no idea... i don't know where to start, but it must be solved using the derivative.

hint: they are asking for acceleration when they say "at what rate... blah blah blah... changing"

and there are wel known aceleation, distance, time equations out there

wouldn't they be asking for velocity or rate, not acceleration?

when there is a rate of change that is synonymous with acceleration

They're asking for the players rate of change of distance, which infers velocity, as opposed to acceleration, which is the rate of change of velocity.

You have your equation set up correctly, why don't you begin by differentiating both sides.

change of rate wrt distance = velocity
change of rate wrt time = acceleration

so sue me.

i don't care that you were wrong, i just have no idea where to start? and I am not sure i understand the notation..

Do you know how to differientiate both sides of the equation you posted? You'll want to include the derivative notation for each variable when you do this.

For example, if I had $$2x^2 = c^3$$ and I differientiated both sides, I would have $$4x \frac{dx}{dt} = 3c^2 \frac{dc}{dt}$$.

i know how to differentiate both sides, but i don't even have two sides...

In your opening post, you had the equation "a^2+b^2=C^2," right? There are two sides to this equation.

i don't understand how that works? but it would be:

60^2 + 90^2 = C^2

You'll want to wait until the very end to plug in your values. Just begin by treating "a," "b," and "c" as variables, and take the derivative of both sides of the equation with respect to time.

2a + 2b = 2c?

it seems like the type of problem where first you do a derivative

and then once you have a resultant equation you plug in 30 for one of the variables

zelphics said:
2a + 2b = 2c?

This is correct, and sprint is right, you'll want to wait until the very end to plug in values. Your equation is missing three things however, you'll want to include the da/dt, db/dt, and dc/dt terms next to their respective variables. So far so good?

Last edited:
yea so da/dt(2a) + db/dt(2b) = dc/dt(2c)?

Right, so now the 2's cancel out. The problem said that you're dealing with two sides of a square, so how can we relate "a" and "b" ? What's our new equation?

## 1. What is a "Dr/ dt rate/distance problem"?

A "Dr/ dt rate/distance problem" is a type of mathematical problem that involves calculating the rate of change (usually represented as "dr/dt") in a system, given the distance traveled (usually represented as "r").

## 2. How do you solve a "Dr/ dt rate/distance problem"?

To solve a "Dr/ dt rate/distance problem", you need to use the formula "dr/dt = r/t", where "r" is the distance traveled and "t" is the time it took to travel that distance. You also need to make sure that all units are consistent (e.g. if "r" is measured in meters, then "t" should be measured in seconds).

## 3. What are some real-life examples of "Dr/ dt rate/distance problems"?

"Dr/ dt rate/distance problems" can be found in many real-life situations, such as calculating the speed of a moving vehicle, the rate of change in the water level of a swimming pool, or the growth rate of a population over time.

## 4. What kind of mathematical skills are needed to solve a "Dr/ dt rate/distance problem"?

To solve a "Dr/ dt rate/distance problem", you need to have a basic understanding of algebra and geometry, as well as the ability to work with equations and units of measurement. You should also be familiar with the concept of rate of change and how it relates to distance and time.

## 5. Are there any tips or tricks for solving "Dr/ dt rate/distance problems" more efficiently?

One helpful tip for solving "Dr/ dt rate/distance problems" is to always make sure your units are consistent and to convert them if necessary. It can also be helpful to draw a diagram or visualize the problem to better understand the relationship between distance, rate, and time. Finally, practice and repetition can help you become more comfortable with solving these types of problems.

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