a postion vector with an magnitude 10m points to the right and up. its x-componet is 6.0m. what is the value of its y-componet?
To find the value of the y-component of the position vector, given its magnitude and x-component, we can use the Pythagorean theorem and trigonometry.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the magnitude of the position vector (10 m) is the hypotenuse of the right-angled triangle, and the x-component (6.0 m) is one of the other two sides. Let's call the y-component we're trying to find "y".
Using the Pythagorean theorem, we can write the equation:
(6.0 m)^2 + y^2 = (10 m)^2
Simplifying the equation:
36.0 m^2 + y^2 = 100 m^2
Subtracting 36.0 m^2 from both sides:
y^2 = 100 m^2 - 36.0 m^2
y^2 = 64 m^2
Taking the square root of both sides to solve for y:
y = √(64 m^2)
y = 8 m
Therefore, the value of the y-component of the position vector is 8.0 m.