What is the y-component of a vector in the x-y plane whose magnitude is 87.8 and whose x-component is 64.9?
X = 64.9
Y = ?
Z = 87.6 = magnitude or hypotenuse.
X^2 + Y^2 = Z^2
Solve for Y.
To find the y-component of a vector in the x-y plane, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the magnitude of the vector is the hypotenuse. Let's call it "m". The x-component is one side of the triangle. Let's call it "x". We want to find the y-component, which is the other side of the triangle. Let's call it "y".
According to the Pythagorean theorem, we have:
m^2 = x^2 + y^2
Plugging in the values:
87.8^2 = 64.9^2 + y^2
Simplifying:
7694.84 = 4211.01 + y^2
To solve for y^2, we subtract 4211.01 from both sides:
y^2 = 3483.83
To find y, we take the square root of both sides:
y = √3483.83
Calculating it:
y ≈ 59.004
Therefore, the y-component of the vector is approximately 59.004.