vector (V1) is 6.3 units long and points along the negative (X) axis. Vector(V2) is 9.0 units long and points at 55 degree to the positive (X)axis.
1- What are the (X) and (Y) components of (V1) vector ?
2-What are the (X) and (Y) components of(V2) vector ?
3-Determine the magnitude of the sum (V1+V2).
4-Determine the angle of the sum (V1+V2).
i've got the answers of the first three questions
1- 6.3,0
2- 5.2,7.4 units
3- 7.5 units
i tried putting tan-1 y/x
fot the 4th question but i've got the wrong answer
i need a help
I do not agree with your answer to #3, either.
V2 components are (5.16, 7.37)
V1 + V2 has components (11.46,7.37)
V1 + V2 has magnitude = 13.63
Angle of V1 + V2 = tan-1 y/x
= 32.7 degrees
counterclockwise from the +x axis.
To determine the angle of the sum (V1+V2), you can use the arctan function to find the angle between the positive x-axis and the resultant vector.
Here's how you can find the angle:
1. Find the x-component and y-component of the sum (V1+V2):
The x-component of the sum = x-component of V1 + x-component of V2
= -6.3 + 5.2
= -1.1 units
The y-component of the sum = y-component of V1 + y-component of V2
= 0 + 7.4
= 7.4 units
2. Use the arctan function to find the angle:
Angle = arctan(y-component / x-component)
Angle = arctan(7.4 / -1.1)
Angle ≈ -82.7 degrees
Note: The arctan function gives the principal value of the angle in the range (-π/2, π/2), so the angle obtained here (-82.7 degrees) is in the fourth quadrant. If you prefer an angle in the range (0, 360), you can add 360 degrees to the result.
Therefore, the angle of the sum (V1+V2) is approximately 277.3 degrees.
To help you with the fourth question, we need to determine the components of the vectors V1 and V2 first.
1. Components of V1:
Since V1 points along the negative X-axis, its X-component is -6.3 units, and its Y-component is 0 units.
2. Components of V2:
To find the X and Y components of V2, we need to use trigonometry. V2 makes an angle of 55 degrees with the positive X-axis. In this case, the X-component is V2 * cos(angle) and the Y-component is V2 * sin(angle).
So the X-component of V2 = 9.0 * cos(55 degrees) = 5.2 units
And the Y-component of V2 = 9.0 * sin(55 degrees) = 7.4 units
Now, let's move on to the remaining questions:
3. Magnitude of the sum (V1 + V2):
To find the magnitude of the sum of two vectors, we can use the Pythagorean theorem. The magnitude of a vector is given by the square root of the sum of the squares of its components.
The X-component of (V1 + V2) = (-6.3) + 5.2 = -1.1 units
The Y-component of (V1 + V2) = 0 + 7.4 = 7.4 units
Now, we can calculate the magnitude of (V1 + V2):
Magnitude = sqrt((-1.1)^2 + (7.4)^2) = 7.5 units
4. Angle of the sum (V1 + V2):
To find the angle of the sum of two vectors, we can use the inverse tangent function. The angle can be calculated using the formula atan2(Y-component, X-component).
Angle = atan2(7.4, -1.1) ≈ -81.6 degrees
Therefore, the angle of the sum (V1 + V2) is approximately -81.6 degrees.