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).
i really need a help
Of course, I'd be happy to help you with your questions! Let's break it down step by step:
1. To find the components of vector (V1), we need to know its length and direction. We are given that V1 is 6.3 units long and points along the negative X-axis. Since it points in the negative X-axis direction, its X-component is -6.3, and its Y-component is 0 (since it doesn't have a vertical component).
2. Similarly, for vector (V2), we are given its length of 9.0 units and its direction at 55 degrees to the positive X-axis. To find its components, we can use trigonometry. The X-component can be found by multiplying the magnitude (9.0) by the cosine of the angle (55 degrees): X = 9.0 * cos(55°). The Y-component can be found by multiplying the magnitude (9.0) by the sine of the angle (55 degrees): Y = 9.0 * sin(55°).
3. To determine the magnitude of the sum of V1 and V2 (V1 + V2), we need to add their respective X and Y components. So, the X-component of the sum is (-6.3 + (9.0 * cos(55°))), and the Y-component is (0 + (9.0 * sin(55°))). We can use these two components to calculate the magnitude using the Pythagorean theorem: magnitude = sqrt(X^2 + Y^2).
4. Finally, to determine the angle of the sum of V1 and V2, we can use the inverse tangent function (tan^(-1)). The angle can be found by taking the inverse tangent of the Y-component divided by the X-component: angle = tan^(-1)(Y/X). Make sure to convert the result from radians to degrees if needed.
By following these steps, you should be able to solve all the questions. Let me know if you need any further assistance or if you have any other questions!
x = |v| cos theta
y = |v| sin theta.
Everything else is laid out for you. Just plug and chug.
To get started,
|v1| = 6
|v2| = 9