Question

A position vector in the first quadrant has an x-component of 21 m and a magnitude of 35 m. what is the value of its y-component?

Answer 1

The y-component of the position vector in the first quadrant, with an x-component of 21 m and a magnitude of 35 m, is found to be 28 m using the Pythagorean theorem.

Step-by-step explanation:

The student is trying to find the y-component of a position vector in the first quadrant given its x-component and magnitude. To do this, one can use the Pythagorean theorem which relates the x-component, y-component, and the magnitude of the vector. The formula is vector magnitude² = x-component² + y-component². Rearranging this formula to solve for the y-component gives y-component = √(vector magnitude² - x-component²).

Given the x-component is 21 m and the vector magnitude is 35 m, the calculation becomes:

y-component = √(35² - 21²)

y-component = √(1225 - 441)

y-component = √(784)

y-component = 28 m

Hence, the value of the y-component of the position vector is 28 m.

Answer 2

Answer:
y = 28 m

Step-by-step explanation:
To answer this question, we will use Pythagorean theorem.
This is because the givens along with the requirement form a right-angled triangle.
the x-component is one of the sides = 21 m
the required y-component is the other side
the magnitude is the hypotenuse = 35 m
Applying Pythagorean theorem, we will be able to get the value of the y-component as follows:
(magnitude)^2 = (x)^2 + (y)^2
(35)^2 = (21)^2 + (y)^2
(y)^2 = 784
y = 28 m

Hope this helps :)