Final answer:
To find the y-component of the position vector in the first quadrant with an x-component of 30 m and a magnitude of 50 m, you can use the Pythagorean theorem.
Step-by-step explanation:
The position vector in the first quadrant has an x-component of 30 m and a magnitude of 50 m. To find the y-component, we can use the Pythagorean theorem. Since the vector is in the first quadrant, both the x-component and y-component are positive. Using the formula:
a^2 + b^2 = c^2
where a represents the x-component, b represents the y-component, and c represents the magnitude:
30^2 + b^2 = 50^2
Simplifying the equation, we can solve for b:
900 + b^2 = 2500
b^2 = 1600
b = 40 m
Therefore, the position vector in the first quadrant has an x-component of 30 m and a y-component of 40 m.