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
1. V1 = (6.3,180deg).
X1 = hor. = 6.3cos180 = -6.3 Units.
Y1 = ver. = 6.3sin180 = 0 Units
2. V2 = (9,55deg.).
X2 = hor. = 9cos55 = 5.16 Units.
Y2 = ver. = 9sin55 = 7.37 Units.
3.Sum = (X!+X2) + i(Y1+Y2),
Sum = (-6.3+5.16) + i(0+7.37),
Sum = -1.14 + i7.37.
Sum = sqrt((-1.14)^2 + (7.37)^2) = 7.46 Units.
4. tanA = Y/X=7.37 / -1.14 = -6.4649
A = -81.2 deg.,CW.
A = -81.2 + 180 = 98.8 deg.,CCW.
No worries! I'll help you step-by-step with each question.
1. To find the components of vector A, we need to know the length and direction. We are given that vector A is 6.3 units long and points along the negative axis. Since it points along the negative axis, its direction is -x. The x-component of vector A is then -6.3, and since it doesn't have any y-component, the y-component is 0.
2. Similarly, for vector B, we are given that it is 9.0 units long and points at 55° to the positive axis. To find the x-component, we multiply the length (9.0) by the cosine of the angle (55°): Bx = 9.0 * cos(55°) ≈ 5.282. To find the y-component, we multiply the length (9.0) by the sine of the angle (55°): By = 9.0 * sin(55°) ≈ 7.111.
3. To determine the magnitude of the sum of the two vectors (vector C = A + B), we first need to calculate the x and y components of vector C. Add the x-components of vector A and B: Cx = Ax + Bx = -6.3 + 5.282 = -1.018. Add the y-components of vector A and B: Cy = Ay + By = 0 + 7.111 = 7.111. The magnitude of vector C is given by the formula: |C| = √(Cx² + Cy²) = √((-1.018)² + (7.111)²) ≈ 7.187 units.
4. To determine the angle of the sum, we use the tangent inverse function. The angle θ is given by the formula: θ = tan^(-1)(Cy / Cx). Plug in the values: θ = tan^(-1)(7.111 / -1.018) ≈ -85°. The negative sign denotes the direction in relation to the positive x-axis.
I hope this helps! Let me know if you have any further questions.