Time Closest Between Two Objects and Distance

I need some guidance on this one please.

Quote:

At midnight the Titanic is 100km due east of a big iceberg. The Titanic is sailing west at 12 km/hr and the iceberg is moving south at 10 km/hr. What time will the Titanic be closest to the iceberg and what will that distance be? Use the 2nd derivative test to prove the answer is the minimum.

Basically all I have at this point it my variables wrote down and converted to seconds and meters along with a picture. I don't know what to do next, please help. Thank you.

Re: Time Closest Between Two Objects and Distance

Quote:

At midnight the Titanic is 100km due east of a big iceberg. The Titanic is sailing west at 12 km/hr and the iceberg is moving south at 10 km/hr. What time will the Titanic be closest to the iceberg and what will that distance be? Use the 2nd derivative test to prove the answer is the minimum.

let the iceberg be at $\displaystyle (0,0)$ at midnight

titanic position as a function of time ...

$\displaystyle x = 100 - 12t$

$\displaystyle y = 0$

iceberg position as a function of time

$\displaystyle x = 0$

$\displaystyle y = -10t$

use the distance formula to get the distance between the two as a function of time, and minimize.

Re: Time Closest Between Two Objects and Distance

Thank you a lot! Everything clicked after your post!