You are given a vector in the xy plane that has a magnitude of 100.0 units and a y component of -45.0 units. What are the two possibilities for its x component?
100^2=x^2+45^2
solve for x
To find the two possibilities for the x component of the vector, we can use the Pythagorean theorem and trigonometry.
First, let's label the given information:
Magnitude of the vector = 100.0 units
Y component = -45.0 units
We can use the Pythagorean theorem to find the magnitude of the x component:
Magnitude^2 = (x component)^2 + (y component)^2
(100.0)^2 = (x component)^2 + (-45.0)^2
Simplifying this equation gives:
10000.0 = (x component)^2 + 2025.0
Rearranging the equation:
(x component)^2 = 10000.0 - 2025.0
(x component)^2 = 7975.0
Taking the square root:
x component = ±√7975.0
Hence, the two possibilities for the x component of the vector are approximately ±89.34 units.