Vector V1 is 6.29 units long and points along the negative x axis. Vector V2 is 4.23 units long and points at +35.0° to the +x axis.
(a) What are the x and y components of each vector?
(b) Determine the sum V1 + V2.
vx1=-6.29
Vx2=4.23cos35
vy2=4.24sin35 assuming it is from the x axis counterclockwise.
add them.
To determine the x and y components of a vector, we can use trigonometry. The x component represents the projection of the vector onto the x axis, and the y component represents the projection onto the y axis.
(a) Finding the x and y components of V1:
Since V1 points along the negative x-axis, its y component is zero. The x component is the negative value of its length since it points in the negative x direction. Therefore, the components of V1 are:
V1x = -6.29
V1y = 0
Finding the x and y components of V2:
To find the x and y components of V2, we need to use the angle it makes with the positive x-axis. We can use trigonometric functions to find these components.
The x component, V2x, can be obtained by multiplying the magnitude of V2 by the cosine of the angle:
V2x = 4.23 * cos(35°)
The y component, V2y, can be obtained by multiplying the magnitude of V2 by the sine of the angle:
V2y = 4.23 * sin(35°)
Now, let's calculate these values:
V2x = 4.23 * cos(35°)
V2y = 4.23 * sin(35°)
(b) Determining the sum V1 + V2:
To calculate the sum of two vectors, we add their respective x and y components.
The x component of the sum, (V1 + V2)x, is:
(V1 + V2)x = V1x + V2x
The y component of the sum, (V1 + V2)y, is:
(V1 + V2)y = V1y + V2y
Now, let's substitute the values and calculate the sum:
(V1 + V2)x = -6.29 + (4.23 * cos(35°))
(V1 + V2)y = 0 + (4.23 * sin(35°))