Solving Vector Problem: What Went Wrong?

[Miike012]

Posted a picture... the picture consists of the word problem and the triangle is how I interpreted the problem...

Vector A Components: (0,10)
Vector B Components: ( Cos60*6,Sin60*6)

Vector C Components: (Cos60*6 = 3 , Sin60*6 + 10 = 15) ... ( 3 , 15 )

Vector C = (9 + 225) ^(1/2) = 15

The true answer is 5.66...
What did I do wrong?

 

[Hootenanny]

Posted a picture... the picture consists of the word problem and the triangle is how I interpreted the problem...

Vector A Components: (0,10)
Vector B Components: ( Cos60*6,Sin60*6)

Correct up until here.

You want to find vector $C$ such that $B+C = A$. Do you understand why?

Also you should note that the questions asks for the final displacement, which is a vector, not a scalar.

 

[Miike012]

Would the resultant vector be A at (0,10) because that is where the final position lies?

 

[Hootenanny]

Would the resultant vector be A at (0,10) because that is where the final position lies?

Yes, but you want to find $C$

 

[rwisz]

There are a few potential issues with the solution provided. Firstly, it is not clear what the problem is asking for. It appears that the triangle represents a vector addition problem, but it is not stated what the desired result is. This could lead to confusion and potential errors in the solution.

Additionally, the provided solution for Vector C components is incorrect. The components should be (Cos60*6, Sin60*6 + 10) which would result in (3, 15) as stated. However, the calculation for the magnitude of Vector C is incorrect. The correct calculation should be (3^2 + 15^2)^(1/2) = 15.65, not 9 + 225 = 15.

Furthermore, it is important to consider the units being used in the problem. The components for Vector A and B are given in units of length, but the units for Vector C's components are not specified. This could also lead to errors in the solution.

To avoid these types of errors in vector problems, it is important to clearly state what the problem is asking for and to double check all calculations and units. Additionally, it may be helpful to draw a diagram or use vector notation to clearly represent the problem.