Question

A certain vector in the xy-plane has an x-component of 4 m and a y-component of 10 m. It is then rotated in the xy-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)

7.2 m

Magnitude of vector do not change by it's rotation.

Initially: X-component $=4m$

Y-component $=10m$

Finally: X-component $=2\times 4m=8m$

Y-component $=y$

$\Rightarrow \sqrt{4^2+{10}^2}=\sqrt{8^2+y^2}$

$\Rightarrow y=\sqrt{52}=7.2m$