Velocity vector addition problem

[evo13]

Homework Statement

Introduction physics

Relevant Equations

Vector addition

Hello, guys. Interesting riddle here.
I have no idea how to solve it. Tried different methods, but point is answer is always wrong,
exact answer Downriver, at an angle of 53.13(degree) to the bank.
That exercise is from
"Pohl’s Introduction to Physics"

 

[PeroK]

The basic idea is that the velocity of the boat relative to the banks is the vector sum of the velocity of the river relative to the banks and the velocity of the boat relative to the river.

 

[evo13]

Yes, and i can't get a right answer. Basic idea is that velocity of boat and river is the same magnitude, at least as i understand it

 

[PeroK]

Yes, and i can't get a right answer. Basic idea is that velocity of boat and river is the same magnitude, at least as i understand it

Let's see your calculations.

 

[PeroK]

PS The given answer of 53.13 degress is correct.

 

[evo13]

Sorry for the sloppiness, this is just one of the solutions I tried

 

[PeroK]

You know that the river is $600m$ wide and it's $300m$ along the bank from $A$ to $B$. The angle $\alpha$ can be calculated from this geometry.

I.e. $\tan \alpha = 1/2$

You should get the answer from that.

 

[evo13]

You know that the river is $600m$ wide and it's $300m$ along the bank from $A$ to $B$. The angle $\alpha$ can be calculated from this geometry.

I.e. $\tan \alpha = 1/2$

You should get the answer from that.

Yep, i did that. ∠α is 26,565 degrees
AB = sqrt(45) is not relevant, sorry.

 

[PeroK]

Yep, i did that. ∠α is 26,565 degrees
AB = sqrt(45) is not relevant, sorry.

That gives you the direction relative to the bank. The question wants the direction relative to the water, which means you have to do vector addition.

 

[evo13]

Sorry but vector addition is second part of my solving attempt, below horizontal line.
I don't understand what else i can do

 

[PeroK]

PS I don't see how you got 58.3 degrees. You should have got 63.4 degrees upstream as the direction relative to the bank. But, that is independent of the velocity of the river.

 

[evo13]

lets try another explanation, more clear i hope

 

[PeroK]

Okay, I see what you've done. Why would $a = b$?

Note that your diagram is based on the reference frame of the banks. It's difficult to indicate the velocity of the boat relative to the river on that diagram.

Vector addition is the way to go!

 

[evo13]

if not a = b, than c = b. Right?
I tried this also

 

[PeroK]

if not a = b, than c = b. Right?
I tried this also

Neither. Your fundamental problem is that $c$ is from the river's frame of reference and $a$ is from the banks frame of reference. You are mixing vectors from two reference frames in one diagram.

Even if these equations were to hold, they can't be shown in a single diagram.

Use vector addition!

 

[evo13]

Ye, alright. Thank for the help.
I am clearly not understand the question than, English is not my native.

 

[PeroK]

Ye, alright. Thank for the help.
I am clearly not understand the question than, English is not my native.

You do understand the question. You're trying a clever shorcut that doesn't work!