Question

One ship is sailing south at a rate of 5 knots, and another is sailing east at a rate of 10 knots. At 2 P.M. the second ship was at the place occupied by the first ship one hour before. at what time was the distance between the ships not changing.?

Answer 1

Did you draw a picture yet. i find this really helps.

Answer 2

@ChmE

Answer 3

@ChmE ??

Answer 4

So let \(t\) be our variable, and it will represent hours.

Answer 5

what happen next? @wio

Answer 6

Let f(t) be the position of ship sailing south, and g(t) be the position ship sailing east.

Answer 7

f(0) = g(2)

Answer 8

then?

Answer 9

I'm interested in the sol'n as well. How did you come up with f(0) = g(2)

Answer 10

I thought it would be one hour

Answer 11

You're right, it's f(0) = g(1)

Answer 12

@bii17 sry for not responding earlier. I wasn't confident in my sol'n and didn't want to possibly steer you down a wrong path at the risk of confusing you.

Answer 13

ChmE, what is your solution?

Answer 14

@ChmE that's ok.. @wio can i see your solution.. i really dont get the problem..

Answer 15

My solution is to find the position functions, then use the Pythagorean theorem on them to get a 'change in distance' function. Then take the derivative. Then find when that is 0

Answer 16

can you show it step by step ?? @wio

Answer 17

Okay bii17. What is the anti-derivative of 5?

Answer 18

anti derivative??? @wio

Answer 19

I don't understand what the question is asking. Is it looking for at what time is the distance the same as the initial change in distance? Thats how I read it

Answer 20

Yes, what does \(\int5dx\) equal?

Answer 21

we havent discussed it in our class.. no idea

Answer 22

Hmmmm, okay, well let's say that the ship started as position 0, it is moving 5 knots, how many knot-hours has it traveled in t hours?

Answer 23

Let a knot-hour be the distance you travel in an hour at the speed of a knot. Our ship will have traveled 5t

Answer 24

Since distance = speed * time.

Answer 25

So f(t) = 5t. Now g(t) = 2t + c. Where c is the initial position. We don't know it yet, but we can use f(0) = g(1) to find out c.

Answer 26

5(0) = 2(1) + c => c = -2

Answer 27

So g(t) = 2t-2
Are you following?

Answer 28

@wio yes..

Answer 29

Now, since they are traveling perpendicular to each other... how can we find the distance between them with respect to time?