Thursday

August 21, 2014

August 21, 2014

Posted by **Anya** on Wednesday, November 10, 2010 at 1:27am.

Meanwhile, at 12pm Boat B, a pirate ship, is 15 km due West of the dock where boat

A started, and is sailing due East at a constant speed of 15 km/h. If the pirates get

within 10 km of another boat, they will spot it and eventually capture it. Is Boat A

in danger of getting captured by the pirates on Boat B?

- calculus -
**Reiny**, Wednesday, November 10, 2010 at 8:19amMake a diagram showing the ships at t hours after 12:00 pm.

Let D be the position of the dock and A and B the position of the boats.

then DA = 20t km

and BD = (15-15t) km

AB^2 = (20t)^2 + (15-15t)^2

let's find the minimum distance AB

2AB d(AB)/dt = 800t + 2(15-15t)(-15)

= 0 for a minimum of AD

800t - 30(15-15t) = 0

800t - 450 + 450t =

t = 450/1250

t = .36 hours

when t = .36

(AB)^2 = 51.84 + 92.16

AB = √144

= 12

Since they have to be within 10 km to be seen, they are ok.

**Related Questions**

calculus - a boat leaves a dock at 2:00 pm and travels due south at a speed of ...

Calculus - At 2:00PM boat X is heading due west at 15mph towards a dock that is ...

math - a boat leaves a dock at 2:00pm ,heading west at 15 km/h. another boat ...

Calculus - a boat leaves a doct at 2:00pm, heading west at 15km/h. Another boat ...

Calculus - Can anyone help me with these two optimization problems? A boat ...

Physics - A speed boat at rest begins to move in a straight line from a dock. ...

Algebra 1 - A boat towing a water skier leaves a dock and travels east at a ...

Calculus Practice Problems - A boat is pulled into a dock by a rope attached to...

geomety - A boat is heading due east at a constant speed of 35 mi/h. There is an...

Physics - Two boats are heading away from shore. Boat 1 heads due north at a ...