Expert: Paul Klarreich - 1/30/2008

Question
Hi,

I am writing you because I need help with the following problem. I hope you can help me. Thank you in advance.




A hot-air balloon, headed due east at an average speed of 15mph and at a constant altitude of 100 feet, passes over an intersection. Find an expression for the distance d (measured in feet) from the balloon to the intersection t seconds later.

Answer
Questioner:   gio
Category:  Advanced Math
Private:  No
 
Subject:  Math problem (hot balloon)
Question:  Hi,

I am writing you because I need help with the following problem. I hope you can help me. Thank you in advance.

A hot-air balloon, headed due east at an average speed of 15mph and at a constant altitude of 100 feet, passes over an intersection. Find an expression for the distance d (measured in feet) from the balloon to the intersection t seconds later.
.................................
Hi, Gio,

To start, make this conversion:

15 mph = 22.5 ft/sec (approx)

Now draw this picture:

 <---------  22.5t feet----------->
                                  B
 0--------------------------------0
 |
 |
 |
 |
 |100 ft
 |
 |
 |
 |
 |
--+--------------------------------0
 I

Use the Pythagorean Theorem:

IB = sqrt((22.5t)^2 + 100^2)