Final answer:
To find the component form from magnitude and bearings, the task involves calculating the horizontal and vertical components of a vector using trigonometric functions. The vector's magnitude is used along with the bearings, converted to a standard angle, to find these components.
Step-by-step explanation:
When dealing with magnitude and degree in bearings to find the component form, the task is to break down a vector into its horizontal (x-axis) and vertical (y-axis) components. This process is essential in fields such as physics and engineering, where vectors are used to represent quantities that have both magnitude and direction. The magnitude of a vector represents its size or quantity, while the bearing provides the direction based on a compass reading, where North is 0°, East is 90°, South is 180°, and West is 270°.
In mathematical terms, the task involves using trigonometric functions to resolve the vector into its components. If we denote the magnitude of the vector as 'A' and the bearing as θ, we find the x-component (East-West axis) using Ax = A cos θ and the y-component (North-South axis) using Ay = A sin θ. The angle θ must be converted appropriately if not initially given in standard position (measured counterclockwise from East). It's crucial to pay attention to the signs of the components, as they indicate direction (positive for North/East, negative for South/West).
For example, if a vector has a magnitude of 100 units and a bearing of 110°, it has been rotated 110° clockwise from North. To find the component form, we break it down into Ax and Ay. If 0A is the angle measured clockwise from East (which is 180 - 110 = 70°), we calculate Ax as 100 cos(70°) and Ay as 100 sin(70°). These calculations will provide the East and North components, respectively, which are useful in various applications such as calculating the net force on an object or finding the displacement of a body in two dimensions.