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

Options

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

Answer

B

Explanation

`A_(x)= 12m, A_(y)= 8m [vec(A)= A_(x) hat(i) + A_(y) hat(j)]`
Magnitude of vector –
`A= sqrt(A_(x)^(2) + A_(y)^(2)) = sqrt(12^(2) + 8^(2)) = sqrt208m`
After rotation-
`A= sqrt(A_(x)^(2) + A_(y)^(2)) rArr sqrt208 = sqrt(((A_(x))/(2))^(2)+ A._(y)^(2))`
`rArr sqrt208 = sqrt((6)^(2) + A._(y)^(2))`
`rArr A._(y)^(2)= 208- 36= 172`
`rArr A._(y)= sqrt172 = 13.11m`