What direction should the swimmer swim in this problem?

[Oblivion77]

Homework Statement

Here is the problem.

Homework Equations

Va/b = Va - Vb

The Attempt at a Solution

s - swimmer
w - water

Vw = 0.3m/s
Vs/w = 2.5m/s

therefore, Vs - Vw = 2.5m/s
Vs - 0.3m/s = 2.5m/s
Vs = 2.8m/s

Now I am a bit confused at this point. It is asking which direction the swimmer needs to swim. What I have tried to do is draw 1 velocity vector pointing directly upward (the 0.3m/s one) and another pointing 38.66 degrees from the horizontal (I calculated that angle using the dimensions given). Am I on the right course to solving the problem, or am I completely wrong?

 

[tiny-tim]

Hi Oblivion77!

therefore, Vs - Vw = 2.5m/s
Vs - 0.3m/s = 2.5m/s
Vs = 2.8m/s

Nooo …you can't say 2.5 + 0.3 = 2.8 …

relative velocities are vectors, so they add (and subtract) like vectors.

… What I have tried to do is draw 1 velocity vector pointing directly upward (the 0.3m/s one) and another pointing 38.66 degrees from the horizontal (I calculated that angle using the dimensions given). Am I on the right course to solving the problem, or am I completely wrong?

Yes that's fine so far …

now complete the vector triangle …

you know the length and direction of one side, the angle of another side, and the length of the third side …

from that, you should be able to find the other angle(s).

 

[Oblivion77]

Thanks for the response. I was wondering If I have this diagram right?

If it's correct would I just then need to solve for the angles? Sorry the drawing isn't really to scale.

 

[tiny-tim]

HI Oblivion77!

(just got up … :zzz:)

Thanks for the response. I was wondering If I have this diagram right?

If it's correct would I just then need to solve for the angles?

Yes, the diagram is fine (and the arrows are the right way) …

so you know that V_s has length 0.3, and V_w - V_s has length 2.5, and you know one of the angles …

now use the sine rule and the cosine rule.

 

[Oblivion77]

Thanks for the response, doesn't Vw have a length of 0.3 and Vs - Vw = 2.5?

 

[tiny-tim]

oops!

Thanks for the response, doesn't Vw have a length of 0.3 and Vs - Vw = 2.5?

oops! yes, I got them the wrong way round.

 

[Oblivion77]

oops! yes, I got them the wrong way round.

No problem, thanks for the help.