The vector V is given by V = (5.0x-12.0y )m. What is W such that V + W = -5|V|x?
To find the vector W such that V + W = -5|V|, we first need to calculate the magnitude of vector V.
The magnitude of a vector V is given by |V| = sqrt(Vx^2 + Vy^2), where Vx and Vy are the x and y components of vector V.
Given V = (5.0x - 12.0y) m, we can substitute the values into the formula and calculate the magnitude:
|V| = sqrt((5.0)^2 + (-12.0)^2)
= sqrt(25.0 + 144.0)
= sqrt(169.0)
= 13.0 m
Now that we have the magnitude of V, we can find the vector W. Let's assume W is given by W = (Wx, Wy) m.
So, V + W = (-5|V|) can be rewritten as:
(5.0x - 12.0y) + (Wx, Wy) = -5(13.0)
We can equate the x and y components separately:
x component: 5.0x + Wx = -5(13.0)
5.0x + Wx = -65.0
(5.0 + W)x = -65.0
x = -65.0 / (5.0 + W)
y component: -12.0y + Wy = 0
Wy = 12.0y
Wy = 12.0(-65.0 / (5.0 + W))
Wy = -780.0 / (5.0 + W)
Thus, the vector W can be written as W = (-65.0 / (5.0 + W), -780.0 / (5.0 + W)) m.