Register to reply

Rate of change in distance question

by Dr Zoidburg
Tags: distance, rate
Share this thread:
Dr Zoidburg
#1
Apr29-08, 02:40 AM
P: 39
Okay, I'm 99% sure I've got the right answer here, but I just wanted to make certain before I send my assignment in. It's the last question and has been bugging me for the last few days until I had an eureka moment just a few minutes back.
(In case you're wondering, I'm doing my studies by correspondence, so other than course notes and textbooks borrowed from the library I have just the internet and my brains (hah!) to aid me)

1. The problem statement, all variables and given/known data
A baseball diamond has sides 27m long. A player is running from 2nd to 3rd at a speed of 9m/s. When he is 6m away from 3rd, at what rate is the player's distance from home plate changing at that instant?


3. The attempt at a solution
x = distance from home plate to 3rd = 27m
y = distance from player to 3rd = 6m
z = distance from player to home = 27.66m (using pythagoras)
speed of player is change of y over time: dy/dt = 9m/s

[tex]z^{2}[/tex] - [tex]y^{2}[/tex]= [tex]x^{2}[/tex]
differentiate with respect to time:
d/dz[tex]z^{2}[/tex] - d/dy[tex]y^{2}[/tex]= 0 (since x doesn't change over time)

dz/dt*2z - dy/dt*2y = 0
divide by 2:
z*dz/dt - y*dy/dt = 0
sub the above (z, y, dy/dt) into the equation and solve:
dz/dt = 1.95m/s

If this ain't correct, please tell me quickly as I need to post my assignment off asap!
Phys.Org News Partner Science news on Phys.org
Security CTO to detail Android Fake ID flaw at Black Hat
Huge waves measured for first time in Arctic Ocean
Mysterious molecules in space
tiny-tim
#2
Apr29-08, 03:07 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,157
Hi Dr Zoidburg!

Yes, that's fine (but a little messy)!

Try shortening it a bit.

For example, there's no need to define an x (I know it's useful for helping you get to your eureka moment, but once you're there, you can forget it) just say z = y + 729 (or z = √(y + 729)).

And
Quote Quote by Dr Zoidburg View Post
d/dz[tex]z^{2}[/tex] - d/dy[tex]y^{2}[/tex]= 0
doesn't make sense, does it?
Dr Zoidburg
#3
Apr29-08, 06:19 AM
P: 39
yay, got it right! Off to the post office I scurry.

And that other bit just came out poorly due to bad formating. It looks better in my assignment

tiny-tim
#4
Apr29-08, 06:23 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,157
Rate of change in distance question

Quote Quote by Dr Zoidburg View Post
yay, got it right! Off to the post office I scurry.
I thought Dr Zoidburg scuttled ?
Dr Zoidburg
#5
Apr29-08, 08:38 PM
P: 39
whoops. you're right there. scuttled. whoop! whoop! whoop!

"Friends, help! A guinea pig tricked me!"
tiny-tim
#6
Apr30-08, 02:30 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,157
I just did a google search for "A guinea pig tricked me",

and got 5370 hits!


Register to reply

Related Discussions
Interesting rate of change question Calculus & Beyond Homework 14
Related Rate -finding the Rate of Change of an Angle Calculus & Beyond Homework 5
Measuring rate of reaction via rate of temperature change Chemistry 3
Rate of change Introductory Physics Homework 9
Rate of change General Math 3