Vector V1 is 8.98 units long and points along the negative x axis. Vector V2 is 4.00 units long and points at +50.0° to the +x axis.
a) What are the x and y components of each vector?
(b) Determine the sum V1 + V2.
To find the x and y components of each vector, we can use trigonometry. Keep in mind that the x-component represents the horizontal direction (left or right) and the y-component represents the vertical direction (up or down).
a)
For Vector V1:
Since Vector V1 points along the negative x-axis, its y-component is 0 and its x-component is -8.98 (negative because it points in the negative x direction).
For Vector V2:
To find the x-component, we can use the cosine function. The cosine of the angle is equal to the adjacent side (x-component) divided by the hypotenuse (magnitude of the vector). So, the x-component is given by:
x-component = magnitude * cos(angle) = 4.00 * cos(50.0°)
To find the y-component, we can use the sine function. The sine of the angle is equal to the opposite side (y-component) divided by the hypotenuse (magnitude of the vector). So, the y-component is given by:
y-component = magnitude * sin(angle) = 4.00 * sin(50.0°)
b)
To find the sum V1 + V2, we can add the respective components of the vectors. The sum of the x-components gives the x-component of the resultant vector, and the sum of the y-components gives the y-component of the resultant vector.
Sum of x-components = -8.98 + (4.00 * cos(50.0°))
Sum of y-components = 0 + (4.00 * sin(50.0°))
So, the sum V1 + V2 is the vector with x-component equal to the sum of x-components, and y-component equal to the sum of y-components.