Q. The magnitude of the $x$-component of vector $\vec{A}$ is $3$ and the magnitude of vector $\vec{A}$ is $5$. What is the magnitude of the $y$-component of vector $\vec{A}$ ?
Motion in a Plane
Solution:
$\vec{A}=A_{x}\,\hat{i}+A_{y}\,\hat{j}$
Also $A=\sqrt{A^{2}_{x}+A^{2}_{y}}$
Here, $A=5$, $A_{x}=3$
$\therefore 5=\sqrt{\left(3\right)^{2}+A^{2}_{y}}$
Squaring both sides, we get
$25=9+A^{2}_{y}$
or $A_{y}=4$
