Three Displacement Vectors of a Croquet Ball are shown, where A is 20.0 units at 90 degrees, B is 40.0 units at 45.0 degrees, and C is 30.0 at 315 degrees. Find:
a) The resultant in unit-vector notation.
AND
b) The magnitude and direction of the resultant displacement.
Sorry guys, I seriously don't get this thing.
No problem! I'm here to help you understand.
To find the resultant displacement, we can add the three displacement vectors together.
a) First, let's represent the displacement vectors A, B, and C in unit-vector notation. In unit-vector notation, we represent vectors using their magnitudes and directions.
Vector A: 20.0 units at 90 degrees can be represented as A = (20.0 * cos(90°))i + (20.0 * sin(90°))j.
Vector B: 40.0 units at 45 degrees can be represented as B = (40.0 * cos(45°))i + (40.0 * sin(45°))j.
Vector C: 30.0 units at 315 degrees can be represented as C = (30.0 * cos(315°))i + (30.0 * sin(315°))j.
Now, let's calculate the values of A, B, and C in unit-vector notation:
A = 0i + 20.0j,
B = 28.28i + 28.28j,
C = -21.21i - 21.21j.
b) To find the resultant displacement in unit-vector notation, we need to add the vectors A, B, and C:
Resultant (R) = A + B + C
R = (0 + 28.28 - 21.21)i + (20.0 + 28.28 - 21.21)j
= 7.07i + 27.07j.
So, the resultant displacement in unit-vector notation is R = 7.07i + 27.07j.
To find the magnitude and direction of the resultant displacement:
Magnitude (|R|) = sqrt((7.07)^2 + (27.07)^2)
Direction (θ) = arctan(27.07 / 7.07)
So, the magnitude of the resultant displacement is |R| ≈ 28.02 units, and the direction is approximately 76.44 degrees (measured counterclockwise from the positive x-axis).
Therefore, the magnitude and direction of the resultant displacement are approximately 28.02 units at 76.44 degrees.
You are lost in the process of resolving a vector into components, then the addition of those components.
Here is what I suggest. Go to the nearest college bookstore, or Barnes Noble, or such, and get the study guide
Schaum's Outline Series: College Physics. There are a a number, I prefer the one for Scientists and Engineers. This will cost you about 18 dollars, it is first rate with good drawings, take a look.