Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of N 51o W at 14 miles per hour, and the other travels at a bearing of S 56o W at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.

- anonymous

- jamiebookeater

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- anonymous

is it 51 degree north of west

- anonymous

?

- anonymous

A.
20.33 miles
B.
43.25 miles
C.
28.20 miles
D.
22.72 miles
E.
37.19 miles

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## More answers

- anonymous

that doesnt seem reasonable......because it said round your answer to two decimal points. oh answers!

- anonymous

Find x and Y component of speed of each ship

- anonymous

ok so ship a would be 28 miles and shib b would be 34 miles i think

- anonymous

Here How I would solve it ..
Ship 1 travel at 51 degree North of West
Using standard coordinate system
X component of speed is -cos(51)*14
Y component of speed is sin(51)*14

- anonymous

This is just ship 1

- anonymous

okay

- anonymous

try this with ship 2

- anonymous

so you will get speed of two ship

- anonymous

Multiply x and Y component of each ship seperately to find position
then just use distance formula

- anonymous

ok so
ship a is -97.49
ship b is 128.6
?

- anonymous

X position of Ship 1 at noon(12-10am)
-cos(51)*14 mile per hours * 2hour
-17.62
Y position of Ship 2 at noon
sin(51)*14*2=21.76

- anonymous

X position of Ship 2
-cos(56)*17*2=something
Y position of Ship 2
-sin(56)*17*2=something
Distance Formula
\[\sqrt(ship 1 (x) position - ship 2( x) position)^2+ship 1 (y) position - ship 2( y) position)^2)\]

- anonymous

X position of Ship 2
-cos(56)*17*2=-23.89
Y position of Ship 2
-sin(56)*17*2=17.73

- anonymous

so then I just plug those into the formula?

- anonymous

I got 19.01 for x position of ship 2

- anonymous

hmmm ok you're probably right

- anonymous

Yep

- anonymous

can you see the distance formula in full

- anonymous

no

- anonymous

it is basically
square root of (xposition of ship 1- xpos ship 2)^2 + (ypos ship 1-y pos ship 2)^2)

- anonymous

Is it physics or math?

- anonymous

math trig/pre calc

- anonymous

Were you able to get answer

- anonymous

?

- anonymous

ok I have to go back to the begining and replug in stuff cause i messed something up hold on

- anonymous

I will do the same thing

- anonymous

ok thanks

- anonymous

I got 45.73.....?

- anonymous

The answer is 37.19

- anonymous

I read that problem wrong it is 51 degree west of north ---- not north of west
so I have to switch sin to cos vice versa

- anonymous

okay I have no clue what i did then

- anonymous

Ship 1 position
X: - sin(51)*14*2 -- A
Y: cos(51)*14*2 --B
Ship 2 position
X: -sin(56)*17*2 -- C
Y: -cos(56)*17*2 --D

- anonymous

okay

- anonymous

sqrt((A-C)^2+(B-D)^2)

- anonymous

=37.19

- anonymous

ok thank you!

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