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 is V1x & V1y
(b) what is the magnitude & direction (degrees)
***im confused on what my x & y is to plug into the magnitude equation***
see my last post.
To answer the questions, we need to understand the components of each vector.
For vector V1, which points along the negative x-axis:
- V1x represents the magnitude of the vector in the x-direction.
- V1y represents the magnitude of the vector in the y-direction.
Since V1 points along the negative x-axis, V1x will be negative, and V1y will be zero.
For vector V2, which forms an angle of 35.0° with the positive x-axis:
- V2x represents the magnitude of the vector in the x-direction.
- V2y represents the magnitude of the vector in the y-direction.
To find V2x and V2y, we can use trigonometry. Since the angle is given, we can use the cosine and sine functions. The trigonometric functions can be defined as follows:
- cos(angle) = adjacent / hypotenuse
- sin(angle) = opposite / hypotenuse
In this case, the hypotenuse is the magnitude of vector V2 (4.23 units).
(a) To find V2x:
- V2x = cos(angle) * magnitude
- V2x = cos(35.0°) * 4.23
(b) To find V2y:
- V2y = sin(angle) * magnitude
- V2y = sin(35.0°) * 4.23
Once you calculate V2x and V2y, you can move on to finding the magnitude and direction.
The magnitude of a vector can be computed using the Pythagorean theorem:
- magnitude = square root of (Vx^2 + Vy^2)
To find the direction in degrees (angle with the positive x-axis), you can use the atan2 function (arctangent).
- direction = atan2(Vy, Vx)
Now let's calculate the values:
(a) V1x:
V1x points along the negative x-axis, so it will be -6.29.
V1y has no magnitude since V1 points only along the x-axis, so V1y = 0.
(b) For V2:
V2x:
V2x = cos(35.0°) * 4.23
V2y:
V2y = sin(35.0°) * 4.23
To find the magnitude:
magnitude = square root of (V2x^2 + V2y^2)
To find the direction:
direction = atan2(V2y, V2x)
Now you can substitute the values into the equations and calculate V1x, V1y, magnitude, and direction.