Question

C,1900km at an angle of 40°from the vertical? What is vector resolve?

Answer 1

Vector resolution refers to breaking a vector into its horizontal and vertical components using trigonometry. The horizontal component is found by multiplying the vector's magnitude by the cosine of the angle, and the vertical component is calculated using the sine of the angle.

Step-by-step explanation:

To understand what 'vector resolve' means in the context of the student's question, we need to discuss vector resolution in physics. Vector resolution is the process of breaking down a vector into its component parts, usually along the perpendicular axes of a coordinate system such as the x and y-axes.

In the given example of resolving a vector representing a 1900 km displacement at an angle of 40° from the vertical, one would use trigonometric relationships to find the horizontal (x) and vertical (y) components of the displacement. If we denote the displacement vector as C:

• The horizontal component would be Cx = C * cos(40°)
• The vertical component would be Cy = C * sin(40°)

The horizontal component is found by multiplying the vector's magnitude by the cosine of the angle, and the vertical component by the sine of the angle, considering the angle is measured from the vertical in this scenario. While these calculations do not give us the precise numeric answer, this is the method one would use to resolve a vector into its scalar components.

Answer 2

When you resolve a vector of 1900 km at an angle of 40° from the vertical, the vertical component is approximately 1222.38 km, and the horizontal component is approximately 1454.83 km.

To resolve a vector into its vertical and horizontal components, you'll want to use trigonometry, specifically the sine and cosine functions.

Let's say you have a vector of magnitude 1900 km at an angle of 40° from the vertical.

The vertical component (V) can be found using the sine function
`(\(\sin\))` since it is opposite the angle:

`\[ V = \text{Magnitude} * \sin(\text{angle}) \]`

`\[ V = 1900 * \sin(40^\circ) \]`

`\[ V \approx 1222.38 \text{ km} \]`

The horizontal component
`(\(H\))` can be found using the cosine function
`(\(\cos\))` since it is adjacent to the angle:

`\[ H = \text{Magnitude} * \cos(\text{angle}) \]`

`\[ H = 1900 * \cos(40^\circ) \]`

`\[ H \approx 1454.83 \text{ km} \]`