You are given a vector in the xy plane that has a magnitude of 84.0 units and a y component of -49.0 units.
Assuming the x component is known to be positive, specify the vector V which, if you add it to the original one, would give a resultant vector that is 71.0 units long and points entirely in the - x direction.
I already solved that the x component is 68.2
Assuming the x component is 68, then
V+68x-49y= -71x
which means V= -71x-68x+49y
fail...
34.4
Vo = 84[Ao]. = Initial vector.
Y = 84*sin A.
-49 = 84*sin A,
A = -35.7o = 35.7o S. of E.
Vo = 84[-35.7o].
X = 84*Cos(-35.7) = 68.
Y = -49(given).
68 - 49i + V = -71.
V = -71-68 + 49i = -139 + 49i = 147.4[-19.42o] = 147.4[19.42] N. of W.
To find the vector V that, when added to the original vector, gives a resultant vector that is 71.0 units long and points entirely in the -x direction, we can use vector addition and subtraction.
First, let's analyze the given information:
- The original vector has a magnitude of 84.0 units and a y component of -49.0 units.
- The resultant vector after adding vector V is 71.0 units long and points in the -x direction.
Since the x component of the original vector is known to be positive and we want the resultant vector to point in the -x direction, the x component of vector V should be negative.
To determine the x component of vector V, we can use the magnitude and x component of the resultant vector, which is 71.0 units and 0.0 units, respectively.
The x component of vector V can be calculated as follows:
x component of V = x component of resultant vector - x component of original vector
x component of V = 0.0 - (68.2) (since the x component of the original vector is known to be 68.2 units)
Hence, the x component of vector V is -68.2 units.
To determine the y component of vector V, we can use the y component of the resultant vector and original vector, which are both 0.0 units.
The y component of vector V can be calculated as follows:
y component of V = y component of resultant vector - y component of original vector
y component of V = 0.0 - (-49.0) (since the y component of the original vector is known to be -49.0 units)
Hence, the y component of vector V is 49.0 units.
Therefore, the vector V is (-68.2, 49.0) units.