Velocity vector addition problem

In summary, the question is asking for the direction of the boat relative to the water. The answer is given by vector addition.
  • #1
evo13
8
0
Homework Statement
Introduction physics
Relevant Equations
Vector addition
1.png


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"
 
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  • #2
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.
 
  • #3
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
 
  • #4
evo13 said:
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.
 
  • #5
PS The given answer of 53.13 degress is correct.
 
  • #6
1637226208606.png


Sorry for the sloppiness, this is just one of the solutions I tried
 
  • #7
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.
 
  • #8
PeroK said:
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.
 
  • #9
evo13 said:
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.
 
  • #10
Sorry but vector addition is second part of my solving attempt, below horizontal line.
I don't understand what else i can do
 
  • #11
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.
 
  • #12
lets try another explanation, more clear i hope
c5cbf771-1fba-492b-bee5-20fdedb30cc2.jpg
 
  • #13
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!
 
  • #14
if not a = b, than c = b. Right?
I tried this also
 
  • #15
evo13 said:
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!
 
  • #16
Ye, alright. Thank for the help.
I am clearly not understand the question than, English is not my native.
 
  • #17
evo13 said:
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!
 

FAQ: Velocity vector addition problem

What is a velocity vector addition problem?

A velocity vector addition problem is a mathematical problem that involves adding or combining two or more velocity vectors to determine the resulting velocity.

How do you solve a velocity vector addition problem?

To solve a velocity vector addition problem, you need to break down each velocity vector into its horizontal and vertical components. Then, add the horizontal components together and the vertical components together. Finally, use the Pythagorean theorem to find the magnitude and the inverse tangent function to find the direction of the resulting velocity vector.

What are some real-world applications of velocity vector addition problems?

Velocity vector addition problems are commonly used in physics and engineering to calculate the resulting velocity of an object that is moving in multiple directions. They are also used in navigation and aeronautics to determine the velocity and direction of an aircraft or spacecraft.

Can velocity vector addition problems have negative solutions?

Yes, velocity vector addition problems can have negative solutions. This occurs when the resulting velocity vector is in the opposite direction of the initial velocity vectors. Negative solutions are common in physics and can represent deceleration or a change in direction.

What are some common mistakes to avoid when solving velocity vector addition problems?

Some common mistakes to avoid when solving velocity vector addition problems include forgetting to break down the velocity vectors into their components, using the wrong trigonometric functions to find the magnitude and direction, and forgetting to account for negative solutions. It is also important to pay attention to units and make sure they are consistent throughout the problem.

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