Data:
theta_1 = 44.9 theta_2 = 146.1
A = 4.8 cm B = 8.7 cm
A)What is the x component of vector A?
B)What is the y component of vector A?
C)What is the x component of vector B?
D)What is the y component of vector B?
E)What is the magnitude of vector (A + B)?
I suppose theta 1 goes with A and theta 2 goes with B ?
I suppose theta is angle counterclockwise from +x axis?
If so:
Ax = 4.8 cos 44.9
Ay = 4.8 sin 44.9
Bx = 8.7 cos 146.1
By = 8.7 sin 146.1
(A+B)x = Ax + Bx
(A+B)y = Ay + By
|A+B| =sqrt[ (A+B)x^2 + (A+B)y^2 ]
For part E which x and y do I plug in?
Part E is this:
|A+B| =sqrt[ (A+B)x^2 + (A+B)y^2 ]
I know but which values do I plug in?
To find the x and y components of a vector, you can use the formulas:
x = magnitude * cos(theta)
y = magnitude * sin(theta)
Let's calculate each component one by one.
A) What is the x component of vector A?
Given magnitude A = 4.8 cm and angle theta_1 = 44.9 degrees.
Using the formula, the x component of vector A can be calculated as:
x_A = 4.8 cm * cos(44.9 degrees)
B) What is the y component of vector A?
Using the same formula, the y component of vector A can be calculated as:
y_A = 4.8 cm * sin(44.9 degrees)
C) What is the x component of vector B?
Given magnitude B = 8.7 cm and angle theta_2 = 146.1 degrees.
Using the formula, the x component of vector B can be calculated as:
x_B = 8.7 cm * cos(146.1 degrees)
D) What is the y component of vector B?
Using the same formula, the y component of vector B can be calculated as:
y_B = 8.7 cm * sin(146.1 degrees)
E) What is the magnitude of vector (A + B)?
To find the magnitude of the sum of two vectors, you can use the formula:
magnitude_AB = sqrt((x_A + x_B)^2 + (y_A + y_B)^2)
Calculate the individual components of A and B in steps A through D. Then substitute those values into the formula for magnitude_AB to find the answer.