Tricky Kinematics Problems - Desperately

[RPierre]

Homework Statement

I am new to this board, but I am at my wits end trying to solve this problem. If anyone could provide a somewhat detailed solution i would forever be in debt, thanks!

One car, located at position (-29.9 , 0 ) is traveling at 12.7 m/s ( +x)
Another Car, located at position ( 0, -41.0) is traveling at 6.5 m/s ( +y)

+y Direction
^
|
|
----------> + x direction

Calculate the smallest distance between the two cars

Homework Equations

I created two functions :
p1 (t) = 12.7t - 29.9
p2 (t) = 6.5t - 41.0

Which represent the position of the cars, based on time, relative to the origin

The Attempt at a Solution

Using pythagorean theorom, i concluded the distance between them can be summarized as

d^2 = (p1(t))^2 + (p2(t))^2

Then i Attempt to solve the minumum of this function, which is where i always screw up.

The correct answer to the problem is 22.9 m

 

[tiny-tim]

Welcome to PF!

Hi RPierre! Welcome to PF!

I created two functions :
p1 (t) = 12.7t - 29.9
p2 (t) = 6.5t - 41.0

Which represent the position of the cars, based on time, relative to the origin
…
Using pythagorean theorom, i concluded the distance between them can be summarized as

d^2 = (p1(t))^2 + (p2(t))^2

Then i Attempt to solve the minumum of this function, which is where i always screw up.

Well, that's fine so far.

Show us how you tried to solve it, and then we'll be able to see where the problem is.