Question

A certain vector in the $xy$ plane has an $x$-component of $12m$ and a $y$-component of $8m$. It is then rotated in the $x-y$ plane so that its $x$-component is halved. Then ifs new $y$-component is approximately

• A. 14 m
• B. 13.11 m
• C. 10 m
• D. 2.0 m

Answer 1

Answer: (B)

Let A be vector in $x-y$ plane. Its $x$ and $y$ components are
$A_x=12m$ and $A_y=8m$
$A=\sqrt{A_x^2+A_y^2}$
$=\sqrt{(12{)}^2+(8{)}^2}$
$A=\sqrt{208}m$
When the vector is rotated in $x-y$ plane, then $x$ component become halved and its new y component
$A_y^{\prime }=\sqrt{{\left(\frac{A_x}{2}\right)}^2+A_y^{{}^{\prime }2}}\sqrt{208}=\sqrt{(6{)}^2+A_y^{\prime 2}}$
$A_y^{\prime }=\sqrt{208-36}$
$A_y^{\prime }=\sqrt{172}$
$=13.11cm$