It's in my Exam|Optimization Question|Picture Included

1. Mar 22, 2007

Raza

1. The problem statement, all variables and given/known data
Ship B is going west at 12km\h[W] while Ship A is going south at 9km\h. In the beginning, the distance that they are away from each other is 75km. When will the ships be the closest?

2. The attempt at a solution
$$D^2=(75-12t)^2+(9t)^2$$

$$D^2=5625-1800t-144t^2+81t^2$$

$$D^2=5625-1800t-63t^2$$

$$\frac{dD}{dt}=-1800-126t$$

$$0=-1800-126t$$

$$t=\frac{1800}{-126}$$

And t can't be a negative number.

Last edited: Mar 23, 2007
2. Mar 22, 2007

e(ho0n3

Your diagram is wrong. You have ship A going south and ship B going west. Anywho, to solve this problem, determine an equation that will give you the distance D between ship A and ship B as observed from one of the ships.

3. Mar 22, 2007

Raza

$$D=\sqrt{(75)^2+(x)^2}$$

$$D=\sqrt{5625+x^2}$$

then what?

Last edited: Mar 23, 2007
4. Mar 22, 2007

e(ho0n3

How are you deriving those equations?

5. Mar 22, 2007

e(ho0n3

This equation was better except for an error in the first term on the RHS.

6. Mar 22, 2007

Raza

I saw those equation used in a textbook in a similar question.

What's RHS?

And what do I now after setting up the equation for D?
$$D=\sqrt{(75)^2+(x)^2}$$

$$D=\sqrt{5625+x^2}$$

$$\frac{dD}{dt}=\frac{x}{\sqrt{5625+x^2}}?$$

Is this what I do?

Last edited: Mar 23, 2007
7. Mar 23, 2007

e(ho0n3

It means right hand side.

You have not explained how you derived that equation.

8. Mar 23, 2007

Raza

It's the pythagorean theorem.

9. Mar 23, 2007

e(ho0n3

OK then. Next question: Why did you decide do use it? How are you using it? Does it make sense?

10. Mar 23, 2007

Raza

$$D^2=(75-12t)^2+(9t)^2$$

$$D^2=5625-1800t+144t^2+81t^2$$ *Note that it's +144t2, not -144t2 like before. Just a multiplication error.:uhh:

$$D^2=5625-1800t+225t^2$$

$$\frac{dD^2}{dt}=-1800+450t$$

$$0=-1800+450t$$

$$t=\frac{1800}{450}$$

$$t=4$$

Therefore, The ship will be the closest at 4 hours with the distance of 45km apart.

Last edited: Mar 23, 2007