What would be the resultant vector with an angle of 30° with the +x axis and has a y component of 8.9 Newtons?
To find the resultant vector, we need to use trigonometry and convert the given information into its components.
1. Start by drawing a coordinate system with the +x axis and the +y axis.
2. Since the angle between the resultant vector and the +x axis is given as 30°, draw a line at a 30° angle from the +x axis.
3. From the point where the line intersects the x-axis, draw a perpendicular line to the y-axis. This is the y-component of the vector.
4. The y-component is given as 8.9 Newtons. Mark this on the y-axis.
5. Now, we can find the x-component of the vector using trigonometry. Since we have the hypotenuse (the resultant vector) and the opposite side (the y-component), we can use the sine function to find the x-component.
- sin(angle) = opposite / hypotenuse
- sin(30°) = x-component / 8.9
6. Rearrange the formula to solve for the x-component:
- x-component = 8.9 * sin(30°)
7. Calculate the value:
- x-component = 8.9 * 0.5
- x-component = 4.45 Newtons
8. Now we have the x-component and y-component of the vector. The resultant vector is the vector formed by combining these two components.
- The x-component is 4.45 Newtons in the +x direction.
- The y-component is 8.9 Newtons in the +y direction.
Therefore, the resultant vector has an x-component of 4.45 Newtons and a y-component of 8.9 Newtons.