You are given a vector in the plane that has a magnitude of 86.0 units and a component of -30.0 units.
What are the two possibilities for its component?
sqrt (x^2+y^2)= 86
x^2 + y^2 = 7396
900 + y^2 = 7396
y = +/- 80.6
ohh.. now i've got it
thank you
To find the two possibilities for the y-component, we can use the Pythagorean theorem. The Pythagorean theorem states that the magnitude of a vector can be found by taking the square root of the sum of the squares of its components. So, we have:
magnitude = sqrt(x^2 + y^2)
Given that the magnitude is 86.0 units and the x-component is -30.0 units, we can substitute these values into the equation:
86.0 = sqrt((-30.0)^2 + y^2)
Squaring both sides of the equation, we get:
7396.0 = 900.0 + y^2
Subtracting 900.0 from both sides, we get:
y^2 = 6496.0
To solve for y, we take the square root of both sides:
y = ±sqrt(6496.0)
Hence, the two possibilities for the y-component are y = sqrt(6496.0) and y = -sqrt(6496.0).