# Thread: girl crossing a river

1. ## girl crossing a river

a ship k is travelling at 25 km/h . another ship is h is travelling east at 17 km/h. to an observer on ship h, ship k appears to be travelling north east..<br>find the velocity of ship k<br><br>what I have tried.<br>$\displaystyle &nbsp;Vk = 25cosa i +25sina j$<br>&nbsp; &nbsp; &nbsp; $\displaystyle &nbsp; &nbsp;Vh=17i &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;&nbsp;$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<br>&nbsp; &nbsp; &nbsp; &nbsp;$\displaystyle &nbsp;&nbsp; Vkh= (25cosa-17)i +25sinaj &nbsp;&nbsp;$<br><br>i and j &nbsp;is equal as its in a north east direction&nbsp;<br>25cosa-17=25sina<br>I have a feeling I am going no where<br><br><br><br>

2. ## Re: girl crossing a river

never mind top post
a ship k is travelling at 25 km/h . another ship is h is travelling east at 17 km/h. to an observer on ship h, ship k appears to be travelling north east..find the velocity of ship k

what I have tried. Vk = 25cosa i +25sina j Vh=17i Vkh= (25cosa-17)i +25sinaj
i and j is equal as its in a north east direction
25cosa-17=25sina
I have a feeling I am going no where

3. ## Re: girl crossing a river

Okay, Vk = 25cosa i +25sina j where a is the angle the ships direction makes with the i, therefore, east, direction.
The second ship, h, is moving east at 17 km/h so its velocity vector is 17i The velocity of h relative to k is (17-25cos(a))i- 25sin(a)j. Since that is "north-east" we must have 17- 25cos(a)= -25 sin(a).

Squaring both sides of the equation, $\displaystyle 289- 50cos(a)+ 625 cos^2(a)= 625 sin^2(a)$ Let cos(a)= y. Then $\displaystyle sin^2(a)= 1- cos^2(a)$ so the equation becomes $\displaystyle 290- 50 y+ 625y^2= 625- 625y^2$ or $\displaystyle 1300y^2- 50y- 335= 0$.

4. ## Re: girl crossing a river

I get cos a=.5272289. ( The other answer is negative)
It is not working out for me .
The right answer at the back of the book is 24i+7j

5. ## Re: girl crossing a river

ship h vector + relative vector = ship k vector

$17i + (ai + aj) = (17+a)i + aj$

$(17+a)^2 + a^2 = 25^2$

$a^2+17a-168=0$

$(a+24)(a-7)=0$

$a > 0 \implies a=7$

ship k vector = $24i+7j$

6. ## Re: girl crossing a river

when writing down the vector of ship k should it not be split up into i and j components. when using Vkh=Vk-Vh i was told to always split the vectors into i and j components, but you leave it as 25

7. ## Re: girl crossing a river

first equation's right side is ship k's velocity vector written in component form ...

second line is the magnitude of ship k's velocity vector

$\sqrt{(17+a)^2 + a^2} = |v_k| = 25$

square both sides and solve for $a$