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A wire is bent in a parabolic shape foll...


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`)

A

`(1)/(2)hat(i)`

B

`-(1)/(4)hat(j)`

C

`2hat(j)`

D

`4hat(i)`

Text Solution

Verified by Experts

The correct Answer is:
B
`x=4y^(2)`
`(dx)/(dt)=8y(dy)/(dt)`
`V_(x)=8yV_(y)`
`V_(x)=4`
`a_(x)=0`
`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=1rArr|a_(y)|=(1)/(4)`
`y=1rArr|a_(y)|=(1)/(4)`
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