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?
V1x =
V1y =
V2x =
V2y =
(b) Determine the sum V1 + V2.
Magnitude
Direction ° (counterclockwise from the +x axis is positive)
i need help on this too!
To find the x and y components of each vector, we can use trigonometry. Mathematically, we can relate the magnitudes and angles as follows:
Vx = V * cos(theta)
Vy = V * sin(theta)
(a) For Vector V1:
Since it points along the negative x-axis, the angle theta is 180 degrees or pi radians. Hence, the components are:
V1x = V1 * cos(180°) = V1 * cos(pi) = V1 * (-1) = -6.29
V1y = V1 * sin(180°) = V1 * sin(pi) = V1 * 0 = 0
For Vector V2:
Given that it points at +35.0° to the +x axis, the components can be found as follows:
V2x = V2 * cos(35.0°)
V2y = V2 * sin(35.0°)
Now, substituting the given values:
V2x = 4.23 * cos(35.0°)
V2y = 4.23 * sin(35.0°)
To find the values of V2x and V2y, you can use a calculator to evaluate the trigonometric functions with the given angle.
(b) To find the sum V1 + V2, simply add the x and y components separately:
Vx_sum = V1x + V2x
Vy_sum = V1y + V2y
Finally, the magnitude of the sum is:
Magnitude = sqrt(Vx_sum^2 + Vy_sum^2)
And the direction can be determined using the inverse tangent function:
Direction = atan2(Vy_sum, Vx_sum) * (180 / pi)
To get the result, substitute the respective values into the equations.