Find the Magnitude of b Given c and a Vector in the Positive y-Axis

[emmy]

Homework Statement

If b is added to c = 3.9i + 3.7j, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of c. What is the magnitude of b?

2. The attempt at a solution
I've probably just been staring at these problems for too long...

First of all, is it valid to say the magnitude of a is the sum of the magnitudes of b and c, that is a=b+c ?

Because if so, then c=sqrt(3.9^2+3.7^2)=a

and if a=b+c then b=a-c= 0 ... which is wrong ):

so what should I do?

 

[supratim1]

since b + c is along y axis, so x-component of (b+c) is 0. therefore, tell me what should be the x-component of b?

Welcome to Physics Forums, Emmy!

 

[emmy]

since b + c is along y axis, so x-component of (b+c) is 0. therefore, tell me what should be the x-component of b?

Welcome to Physics Forums, Emmy!

Thanks so much! (and thanks for replying too :] )

If b+c=0 then bx would have to be -cx, or -3.9?
and then since the y component of b+c equals the y component of c, the y component of b is 0

then you plug into the equation: magnitude of b= sqrt((-3.9)^2+(0)^2)= 3.9 units?

 

[supratim1]

b = -3.9i + Yj (let)

so b + c = (Y + 3.7)j

since magnitudes equal, equate magnitude of c with (Y+3.7), you will find the answer.

 

[rwisz]

As a scientist, your response would be to first clarify the question by asking for more information. It is not clear what the variables a and b represent in this scenario. Are they vectors or scalars? Are they related to c in any way?

Assuming that a and b are also vectors, and that the statement is referring to the magnitude of the resulting vector when b is added to c, then we can use vector addition to find the magnitude of b.

Let's represent b as a vector in the form b = bi + bj. Since the resulting vector is in the positive direction of the y-axis, we know that the x-component of b (bi) must be zero. Therefore, we can rewrite b as b = 0i + bj = bj.

Now, using vector addition, we can say that c + b = a. Substituting in the values given for c, we get (3.9i + 3.7j) + (0i + bj) = a = (3.9 + 0)i + (3.7 + b)j.

Since we know that the magnitude of a is equal to the magnitude of c, we can set up an equation to solve for b:

|c| = |a|

√(3.9^2 + 3.7^2) = √((3.9 + 0)^2 + (3.7 + b)^2)

Simplifying this equation, we get:

√(3.9^2 + 3.7^2) = √(15.21 + 13.69 + 7.4b + b^2)

Squaring both sides, we get:

15.21 + 13.69 = 15.21 + 13.69 + 7.4b + b^2

Rearranging the terms, we get:

7.4b + b^2 = 0

Solving for b, we get two solutions: b = 0 or b = -7.4. However, since we know that b must be a positive value (since it is in the positive direction of the y-axis), the only valid solution is b = 7.4.

Therefore, the magnitude of b is 7.4.