- NotTim

2 canoeists, A & B, live on opposite shores of a 300.0 m wide river that flows east at 0.80 m/s. A lives on the north shore and B lives on the south shore. They both set out to visit a mutual friend X who lives on the north shore at a point 200.0m upstream from A and 200.0m downstream from B. both canoeists can propel their canoes at 2.4 m/s thru the water. How much time must canoeist A wait after canoeist B sets out so that they both arrive at X at the same time? Both canoeists make their respective trips by the most direct routes.

- katieb

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- NotTim

This is for a friend, so I don't have much work shown.

- NotTim

I know that B takes 125s.
CALC:
1. v=2.4-0.80=1.6m/s
2. t=200m/1.6m/s=125s

- anonymous

note: 2.4 is speed relative to the earth?

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## More answers

- NotTim

https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-prn1/533567_154212501399299_1017958671_n.jpg
https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-snc7/421635_154212521399297_25972720_n.jpg
https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-prn1/76140_154212481399301_1414230843_n.jpg
https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-ash4/387012_154212484732634_845307988_n.jpg
https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-ash4/428325_154212474732635_582085865_n.jpg
https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-prn1/150879_154212514732631_1274474888_n.jpg
https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/554471_154214558065760_366131359_n.jpg
https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-ash3/44769_154214568065759_779969484_n.jpg
https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-snc7/486007_154214574732425_1940920149_n.jpg
https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-ash3/537274_154214594732423_1396018523_n.jpg
https://fbcdn-sphotos-d-a.akamaihd.net/hphotos-ak-prn1/45480_154216528065563_1014789527_n.jpg

- NotTim

@Shadowys Yes, I believe so.
Those links are images of an answer key I wrote down. Step 5 is indecipherable though. My friend had difficulties understanding the angle.

- anonymous

can i use vectors to solve this?(it should be solved with vectors)

- NotTim

Wait....er. no. My friend's course probably doesn't use vectors.

- anonymous

cos, the speed 2.4 is gonna have it's components...lol...without vectors....

- NotTim

well, go ahead and use vectors if you like. (is this vectors the basic kind, or from calculus and vectors)?

- anonymous

|dw:1359342186714:dw|
the basic kind. where i=unit vector in x direction, j is unit vector in y direction.
the velocity of A, \(\vec v_A = -2.4\vec i +0.8i=-1.6\vec i\)
the displacement vector of A \(\vec S_A= -200\vec i\)
so time taken for average journey = \(\frac{|\vec S_A|}{|\vec v_A|}=\frac{\sqrt{(-200)^2}}{\sqrt{(-1.6)^2}}=125s\)
the angle of BX is \(tan^{-1} 3/2=0.9828 rad \)
for B, velocity of B =\(\vec v_B = 2.4(cos 0.9828 \vec i+sin 0.9828 \vec j)+0.8\vec j=2.1313\vec i + 0.832\vec j\)
displacement is \(\vec S_B= 200\vec i+300\vec j\)
so time taken for average journey = \(\frac{|\vec S_B|}{|\vec v_B|}=\frac{\sqrt{(200)^2+(300)^2}}{\sqrt{(2.1313)^2 +(0.832)^2}}=157.35s\)
so time needed to wait=157.34s-125s=32.35s

- NotTim

answer key says 6.1s.

- anonymous

is my diagram wrong?

- NotTim

|dw:1359314524260:dw| yours is right. just missed a few lines

- NotTim

|dw:1359314590576:dw|

- NotTim

Your part A is fine, its jsut part B

- anonymous

hmm...either it's wrong that i took 2.4 as the magnitude...what do you think?

- NotTim

The first time you used it is fine, but I'ven ever seen the 2nd time 2.4 wasused (usign ctrl-F)

- anonymous

oo, right, i forgot to multiply the j component by 2.4.
so \(\vec v_B =2.1313\vec i + 1.997 \vec j\)
t=123.49s....

- NotTim

Vb here was 131.15s?

- NotTim

Sorry, Tb is 131.15s

- NotTim

125s was an acceptable value too for some reason.

- anonymous

nope.....hmm...am i overthinking this?
for which reason?

- NotTim

125s was an acceptable solution for the time for B.
And why? I do not know. I've looking over various different solutions and methods here (not understanding), and the values 131.15 and 125 are acceptable for some odd reason.

- NotTim

of course, 131.15s is the on on the official answer key

- NotTim

we can give it a rest now if you want.

- anonymous

alright. hopefully someone else will give it a go.

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