The resultant of vectors
A⃗
and
B⃗
has a magnitude of 20 units.
A⃗
has a magnitude of 8 units, and the angle between
A⃗
and
B⃗
is
40o
. Calculate the magnitude of
B⃗
To calculate the magnitude of vector B, we can use the concept of the resultant of vectors.
The resultant vector R is calculated by adding vector A and vector B. The magnitude of the resultant vector R is given as 20 units.
To find the magnitude of vector B, we can use the following formula:
|R| = sqrt((Ax + Bx)^2 + (Ay + By)^2)
Where |R| is the magnitude of the resultant vector R, Ax and Ay are the x and y components of vector A, and Bx and By are the x and y components of vector B.
Since we know the magnitude of vector A (8 units) and the angle between vector A and vector B (40 degrees), we can calculate the x and y components of vector A.
Ax = A * cos(angle)
Ay = A * sin(angle)
Substituting the given values:
Ax = 8 * cos(40)
Ay = 8 * sin(40)
Now we can substitute these values into the formula to calculate the magnitude of vector B:
20 = sqrt((8 * cos(40) + Bx)^2 + (8 * sin(40) + By)^2)
Simplifying this equation and solving for the magnitude of vector B will give you the answer.
8*Cos40 + 8*sin40 + B = 20
6.13 + 5.14i + B = 20
B = 20 - 6.13 - 5.14i
B = 13.87 - 5.14i
B = sqrt(13.87^2+5.14^2)