How to Solve Related Rates Problems with Balloon and Cyclist | 3 Second Increase

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Homework Help Overview

The problem involves related rates, specifically examining the relationship between the height of a rising balloon and the distance of a cyclist moving along a straight road. The scenario describes a balloon rising at a constant speed while a cyclist passes beneath it, with a specific question about the rate of change of distance between them after a set time.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the assignment of variables x and y to the balloon's height and the horizontal distance of the cyclist, questioning the correct interpretation of the initial height of the balloon. There is also a focus on the need for consistency in variable assignment.

Discussion Status

The discussion is active, with participants clarifying variable assignments and engaging in dialogue about the setup of the problem. Some guidance has been provided regarding the interpretation of the initial conditions, but no consensus has been reached on the variable definitions.

Contextual Notes

There is a noted ambiguity regarding the assignment of values to x and y, as well as the initial conditions of the problem. Participants are working within the constraints of the problem statement and their own interpretations.

cmajor47
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Homework Statement


A balloon is rising at a constant speed of 5 ft/s. A boy is cycling along a straight road at a speed of 15 ft/s. When he passes under the balloon, it is 45 ft above him. How fast is the distance between the boy and the balloon increasing 3 seconds later.


Homework Equations


dx/dt=15 ft/s
dy/dt=5 ft/s
c2=x2+y2

The Attempt at a Solution


2c dc/dt = 2x dx/dt + 2y dy/dt
c(dc/dt) = x(dx/dt) + y(dy/dt)
c(dc/dt) = x(15) + y(5)
c(dc/dt) = 15x + 5y
My first problem is: Is the 45ft x or y?
 
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cmajor47 said:
c(dc/dt) = 15x + 5y
My first problem is: Is the 45ft x or y?

Hi cmajor47! Welcome to PF! :smile:

45 ft is the value of y at time 0 (and 0 ft is the value of x at that time).

In your equation, c(dc/dt) = 15x + 5y, c x and y must be the values at time 3. :smile:
 
There was NO "x" or "y" in the original problem! Since you were the one who wrote dx/dt= 5 ft/s and were told "A balloon is rising at a constant speed of 5 ft/s." I guess you were taking x to be the height of the balloon at any given time. What was the height of the balloon at the time in question?
 
Don't I have to assign a letter value to each piece of information? Did I assign them correctly?
 
No one can tell you what letters are "correct"- it is entirely your choice. You just have to be consistent.

What did YOU choose x and y to represent when you set up the equation? What are values of the quantities represented by x and y at the point in time in question?
 
I realized how to solve the problem. Thanks to everyone for their help.
 

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