The Sum Is a Third Vector A, which is directed along an x axis, is to be added to vector B, which has a magnitude of 3.5 m. The sum is a third vector that is directed along the y axis, with a magnitude that is 7 times that of A. What is the magnitude of A
To find the magnitude of vector A, we need to analyze the given information and use some mathematical reasoning.
We know that vector A is directed along the x-axis, and the sum of vector A and vector B forms a third vector directed along the y-axis. Additionally, the magnitude of the third vector along the y-axis is 7 times that of vector A.
Let's break down the information step by step:
1. Vector B has a magnitude of 3.5 m.
2. The sum of vector A and vector B forms a third vector directed along the y-axis.
3. The magnitude of this third vector along the y-axis is 7 times that of vector A.
From point 3, we can say that the magnitude of the third vector along the y-axis is 7A, where A is the magnitude of vector A.
Since the sum of vector A and vector B forms the third vector, we can apply the Pythagorean theorem to find the magnitude of the third vector.
The Pythagorean theorem states that the square of the hypotenuse (the magnitude of the third vector) is equal to the sum of the squares of the other two sides (the magnitudes of vector A and vector B).
Using the Pythagorean theorem, we can write the equation:
(7A)^2 = A^2 + (3.5)^2
Simplifying the equation:
49A^2 = A^2 + 12.25
48A^2 = 12.25
Dividing both sides of the equation by 48:
A^2 = 12.25 / 48
A^2 = 0.255
Taking the square root of both sides:
A ≈ √0.255
A ≈ 0.505 m
Therefore, the magnitude of vector A is approximately 0.505 meters.