Question

A certain vector in the $xy$ plane has an $x$ component of $4m$ and a $y$ component of $10m$. It is then rotated in the $xy$ plane so that its $x$-component is doubled. Then its new $y$ component is (approximately) :

• A. $20m$
• B. $7.2m$
• C. $5.0m$
• D. $4.5m$

Answer 1

The correct option is B $7.2m$

Since the vector only rotates, its magnitude must remain constant.

$x_0^2+y_0^2=x_1^2+y_1^2$

$4^2+{10}^2=8^2+y_1^2$

$y_1^2=52$

$y_1=7.2$