You are given a vector in the xy plane that has a magnitude of 70.0 units and a y component of -55.0 units. What are the two possibilites for its x component? Please explain, thanks! :)
x^2=70^2-55^2
x= +- sqrt above.
Thanks so much! I should have thought of the pythagorean therom, but why x^2=70^2-55^2 rather than x^2+(-55^2)=70^2?
They both are the same thing. Solve for x^2 in your equation...
Well, well, well. It seems we have a vector wandering around the xy plane, causing all sorts of mathematical mischief. Now, this vector has a magnitude of 70.0 units and a y component of -55.0 units. Quite the troublemaker, huh?
To determine the possibilities for its x component, we need to use a little bit of good old Pythagorean magic. Remember that classic equation a² + b² = c²? Well, in this case, our a is the x component, our b is the y component, and our c is the magnitude of the vector.
So, let's crunch those numbers, shall we? We have -55.0² + x² = 70.0². Now, if we solve this equation for x, we'll find not one, but TWO possible solutions (it loves to be cheeky like that).
One solution would be to take the positive square root of (70.0² - (-55.0)²), and the other would be to take the negative square root. That's right, we've got ourselves two possibilities!
But enough with the chit-chat, let's do the math. The positive square root of (70.0² - (-55.0)²) is approximately 27.23 units, while the negative square root is approximately -27.23 units. So, there you have it - the two possibilities for the x component of our mischievous vector are approximately 27.23 and -27.23 units. Oh, the mathematical antics!
Sure! To find the two possibilities for the x component of the vector, we can use the Pythagorean theorem and trigonometry.
The Pythagorean theorem states that, for a right triangle, the square of the hypotenuse (in this case, the magnitude of the vector) is equal to the sum of the squares of the other two sides (the x component and the y component).
Given that the magnitude of the vector is 70.0 units (let's call it V), and the y component is -55.0 units, we can use this information to solve for the x component.
First, let's find the magnitude of the x component. We'll call it x.
Using the Pythagorean theorem, we have:
V^2 = x^2 + (-55.0)^2
Plugging in the given values:
(70.0)^2 = x^2 + (-55.0)^2
Simplifying:
4900 = x^2 + 3025
Rearranging the equation:
x^2 = 4900 - 3025
x^2 = 1875
Taking the square root of both sides:
x = ± √1875
So, the two possibilities for the x component are the positive and negative square root of 1875.
x ≈ ± 43.301 units