1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Related Rates Problem

  1. Jun 29, 2008 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    dx/dt=15 ft/s
    dy/dt=5 ft/s

    3. 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?
  2. jcsd
  3. Jun 29, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    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:
  4. Jun 29, 2008 #3


    User Avatar
    Science Advisor

    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 ballon at any given time. What was the height of the ballon at the time in question?
  5. Jun 30, 2008 #4
    Don't I have to assign a letter value to each piece of information? Did I assign them correctly?
  6. Jun 30, 2008 #5


    User Avatar
    Science Advisor

    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?
  7. Jun 30, 2008 #6
    I realized how to solve the problem. Thanks to everyone for their help.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook