home > q&a board > algebra thru pre-calculus > topic: find a math expression

Q BgQuestion:

Rookie
Karma Points: 0
Respect (97%):
posted by  FDRHS on 7/1/2008 9:58:20 AM  |  status: Live  

Find A Math Expression

Course Textbook Chapter Problem
Precalculus Precalculus (7th) by Sullivan 1 66
Question Details:
A hot-air balloon, headed due east at an average speed of 15 miles per hour 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.
 
 
If you do not know how to answer questions posted or if you are unsure about how to reply, please move on to the next question(s).  A wrong reply will only add to my confusion.  Clear? 

AAnswers:

Answer Question
Sage
Karma Points: 3,740
posted by Betel on 7/1/2008 10:10:02 AM  |  status: Live
Asker's Rating: Lifesaver   
FDRHS's comment:
"Betel is the greatest!"
Response Details:

First, convert mph to feet per second:

15miles/hour * 5280feet/mile * 1hour/3600 seconds = 22 ft/s

    


Now, by Pythagorean Theorem:

d = √{(100ft)2 + [(22ft/s)(t)]2}

Or in a simpler form, noting the answer will come out in feet:





Hope that helps!
When I post a solution I assume you have some level of mathematical sophistication. (For instance, if you post a question about differential equations, I'll assume you know how to take derivatives; if you post an algebra question, I'll try to provide more detail.) If anything doesn't make sense, feel free to PM me for clarification. No amount of degrees can prevent mistakes; if you find one in my work, please let me know.

In the time it took you to read that, the universe expanded by 300 trillion cubic light years :)
Tags: Math, Precalculus
Oracle
Karma Points: 8,353
posted by Ratso Rizzo on 7/1/2008 10:12:57 AM  |  status: Live
Asker's Rating: Helpful   
FDRHS's comment:
"A job well-done!"
Response Details:
First, 15 miles per hour converts to 22 feet per second
 

 
 
By the pythagorean theorem,
d2=1002+(22t)2
d = √(100000+484t2)
Rate me or I'll tell your mom!
Tags: Math, Precalculus
Sage
Karma Points: 4,082
(Maple Leaf International School)
posted by Steve_R on 7/1/2008 10:19:29 AM  |  status: Live
Asker's Rating: Helpful   
FDRHS's comment:
"Your picture is somewhat clear but not as clear as the other two replies. Thanks anyway."
Response Details:
As a point of reference, assume that at t = 0 hours, the balloon is directly over the intersection.
 
At some time t1, the balloon is at position x1 relative to intersection
 
At some time t2, the balloon is at position x2 relative to intersection
 
At any time 't', the balloon is at position 'x' relative to intersection
 
 
 
Relative to the air, the balloon covers dair = *15 mph * 5280 miles / feet) * 1 hour / 3600 s) * t     
 
                                                               = 22 t     where 'd' is in feet  and t in seconds
 
Relative to ground,  dground = x = √(1002 + (22 t)2
 
                                                  = √(10000 + 484 t2)
 
 
Get with the program and get with Cramster! 
Tags: Math, Precalculus
Answer Question
Ask New Question

Join Cramster's Community

Cramster.com brings together students, educators and subject enthusiasts in an online study community. With around-the-clock expert help and a community of over 100,000 knowledgeable members, you can find the help you need, whenever you need it. Join for free today » How Cramster is different than tutoring »

Need Help In

Useful Links