Questions: Vector A, of magnitude 360.5 and direction θ=212.23°, has x - and y-components -305.0 and -192.3. See the figure to the right. Change 212.23° to 180.00° and find the components of the vector. The horizontal component is (Round to one decimal place as needed.)

Vector A, of magnitude 360.5 and direction θ=212.23°, has x - and y-components -305.0 and -192.3. See the figure to the right. Change 212.23° to 180.00° and find the components of the vector.

The horizontal component is
(Round to one decimal place as needed.)

Transcript text: Vector $A$, of magnitude 360.5 and direction $\theta=212.23^{\circ}$, has $x$ - and $y$-components -305.0 and -192.3. See the figure to the right. Change $212.23^{\circ}$ to $180.00^{\circ}$ and find the components of the vector. The horizontal component is $\square$ (Round to one decimal place as needed.)

Solution

Solution Steps

Step 1: Find the angle with respect to the positive x-axis

The problem states to change the direction to 180.00°. This angle is already with respect to the positive x-axis.

Step 2: Calculate the x-component

The x-component of the vector A can be calculated using the following formula: Ax = A * cos(θ) Where A is the magnitude of the vector (360.5) and θ is the angle with respect to the positive x-axis (180.00°). Ax = 360.5 * cos(180°) Ax = -360.5

Step 3: Calculate the y-component

The y-component of the vector A can be calculated using the following formula: Ay = A * sin(θ) Where A is the magnitude of the vector (360.5) and θ is the angle with respect to the positive x-axis (180.00°). Ay = 360.5 * sin(180°) Ay = 0