A wire is bent in a parabolic shape followed by equation `x=4y^(2)` consider origin as vertex of parabola a wire parallel toy axis moves with constant speed 4m/s along x-axis in the plane of bent wire. Then the acceleration of touching point of straight wire and parabolic wire is (when straight wire has x coordinates `=4m`)

Options

A. `(1)/(2)`
B. `(1)/(4)`
C. `2`
D. `4`

Explanation

`x=4y^(2)`
`(dx)/(dt)=8y(dy)/(dt)`
`V_(x)=8yV_(y)`
`V_(x)=4`
`a_(x)=0` ltbr. `0=a_(x)=8[y.a_(y)+V_(y)^(2)]`
`-ya_(y)=V_(y)^(2)`
`|a_(y)|=(v_(y)^(2))/(y)`
`|a_(y)|=(v_(x)^(2))/(64y^(3))=(16)/(64xxy^(3))`
at `y=1implies|a_(y)|=(1)/(4)`