Question

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

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

Answer 1

Answer: (B)

Here, $A =4 i +10 j$
$\therefore | A |=\sqrt{(4)^{2}+(10)^{2}} =\sqrt{16+100} $
$=\sqrt{116}\, m$
Now, according to question,
$A =8 i +n j$
So, $| A |=\sqrt{(8)^{2}+n^{2}}$
$\therefore \sqrt{116}=\sqrt{(8)^{2}+n^{2}}$
squaring both sides
$116 =64+n^{2} $
or $n^{2} =116-64=52$
or $n=7.2\, m$