Vector is 6.3 units long and points along the negative axis. Vector is 9.0 units long and points at 55 to the positive axis.
1- What are the and components of vector ?
2-What are the and components of vector ?
3-Determine the magnitude of the sum .
4-Determine the angle of the sum .
i've tried to solve it but i don't really get it.. im stuck
that's right
here is the question
Vector (V1) is 6.3 units long and points along the negative (X) axis. Vector(V2) is 9.0 units long and points at 55 degree to the positive (X)axis.
1- What are the (X) and (Y) components of (V1) vector ?
2-What are the (X) and (Y) components of(V2) vector ?
3-Determine the magnitude of the sum (V1+V2).
4-Determine the angle of the sum (V1+V2).
No worries! I'd be happy to help you understand and solve these problems step by step.
1. To find the x and y components of Vector 1, we first need to determine its direction. Since it points along the negative x-axis, we know the x component will be negative and the y component will be zero. Therefore, the x component of Vector 1 is -6.3 and the y component is 0.
2. To find the x and y components of Vector 2, we need to use the given angle. Since the vector makes an angle of 55 degrees with the positive x-axis, we can decompose it into its x and y components using trigonometry. The x component would be the adjacent side, and the y component would be the opposite side. To find these components, we use the following formulas:
x component = magnitude * cos(angle)
y component = magnitude * sin(angle)
Applying the formulas:
x component = 9.0 * cos(55°) ≈ 5.053
y component = 9.0 * sin(55°) ≈ 7.202
Therefore, the x component of Vector 2 is approximately 5.053, and the y component is approximately 7.202.
3. To determine the magnitude of the sum of two vectors, we can use the Pythagorean theorem. The magnitude of a vector is the square root of the sum of the squares of its components. In this case, we want to find the magnitude of the sum of Vector 1 and Vector 2. The formula to calculate the magnitude of the sum is:
magnitude = √(x1^2 + y1^2) + √(x2^2 + y2^2)
where (x1, y1) are the components of Vector 1 and (x2, y2) are the components of Vector 2.
Applying the formula:
magnitude = √((-6.3)^2 + 0^2) + √(5.053^2 + 7.202^2) ≈ 11.543
Therefore, the magnitude of the sum of Vector 1 and Vector 2 is approximately 11.543 units.
4. To find the angle of the sum of two vectors, we can use the inverse trigonometric functions. The angle can be calculated using the formula:
angle = arctan(sum of y components / sum of x components)
Applying the formula:
angle = arctan((0 + 7.202) / (-6.3 + 5.053)) ≈ 117.4°
Therefore, the angle of the sum of Vector 1 and Vector 2 is approximately 117.4 degrees.
You have omitted some symbols and words, with the result that your question does not make sense.
Apparently you are adding two vectors. They should be given different labels.
In 1 and 2, you also omitted a word after "the".
You apparently also omitted the word "degrees" (or the symbol) after "55".