Question

At noon, ship a is 150km west of ship b. ship a is sailing east at 35 km/h and ship b is sailing north at 25 km/h. how fast is the distance between the ships changing at 4 pm

Answer 1

would i just take \[\Delta y / \Delta x \]

Answer 2

you want dr/dt; so implicit this thing with respect to time..

your formula is the pythag thrm

Answer 3

your dy/dt, or rather the d'north'/dt = 25; and d'e'/dt = 35

Answer 4

e^2 + n^2 = r^2

Answer 5

e' 2e + n' 2n = r' 2r ; divide it all by 2

e' e + n' n = r' r

r' = [e' e + n' n]/ r

Answer 6

ok so if i take that and introduce log i have f(x)+f'(x) which is

Answer 7

log?

Answer 8

\[e^2+n^2-r^2+ 1/2x +1/2n +1/2r\]

Answer 9

well ln

Answer 10

draw a triangle a right triangle with sides:

n = 4(25); e = 4(35)+150; solve the pythag thrm for r

r = sqrt(100^2 + e^2) :)

Answer 11

there is no call for any log or ln in this problem... your thinking to much at it :)

Answer 12

ok i am agreeing with using the pythag but i question your 4(35)+15 because of the direction of sail for the boat

Answer 13

well 4(35)+150

Answer 14

\[r' = \frac{35(e) + 25(n)}{\sqrt{100^2 + e^2}}\]

Answer 15

because the boat is to the west and sailing east wouldn't it be 4(35)-150?

Answer 16

ok let me work that out really fast

Answer 17

150 + 4hours worth of 35 is.....150 + 4(35) :)

Answer 18

....maybe, i coulda read it wrong lol

Answer 19

ok for your r' i am showing 140.9996308

Answer 20

your right; 4(35) - 150 :)

Answer 21

2850
------
sqrt(100^2 + 10^2) = sqrt(10100)

r' = 28.358 is what I get

Answer 22

ok if i use the reg pythag a^2+b^2=c^2 will i end up with the right answer after i solve the correct values

Answer 23

i just renamed the variables to keep track of them better; I know east is 35 and n is 25, so to keep the variables in shape I just rename them n and e

Answer 24

ok i did the same thing as you and ended up with a different number i am trying to work back to your answer

Answer 25

n = 100; n' = 25; n n' = 2500

e = 10; e' = 25; e e' = 250

Answer 26

r = sqrt(100^2 + 10^2)

r = sqrt(10000 + 100)

r = sqrt(10100)

Answer 27

when i do sqrt(10100) i end up with 100.4987562

Answer 28

crap lol.....n' = 35 ;) e e' = 350

Answer 29

ok little off track here why are we breaking down the east and north into double derives?

Answer 30

its hard to keep up with my typos with my computer lagging so much...... you need to read thru them :)

Answer 31

we derive implicitly with respect to time; so all our derived bits stay intact

Answer 32

e^2 + n^2 = r^2 ; implicit with respect to "t"

Answer 33

e' 2e + n' 2n
----------- = r' = dr/dt = how fast the boats
r are moving away from each other

Answer 34

thats 2r under there :) but all the twos factor out to 1 so they can dissapear

Answer 35

e' e + n' n
----------- = r' = dr/dt
r

Answer 36

fantastic answer as always amistre, thanks a ton for the help

Answer 37

35(10) + 25(100)
---------------- = r' = dr/dt
sqrt(10100)

Answer 38

youre welcome :)

Answer 39

2850
---------- = 28.3585
sqrt(10100)

Answer 40

yup i agree our math was jiving on that last answer