A particle moves in xy plane. The rate of changes of `theta` at time t=2 second ( where `theta` is the angle which its velocity vector maks with positive x-axis) is

Options

A. `2/17rad//s`
B. `1/14 rad//s`
C. `4/7rad//s`
D. `6/5rad//s`

Answer

a

Explanation

`x=2timplies v_(x)=(dx)/(dt)=2`
`Y=2t^(2)implies v_(y)=(dy)/(dt)=4t`
`:. Ttan theta =(v_(y))/(v_(x))=(4t)/2=2t`
Differentiating with respect to time we get,
`(sec^(2) theta)(d theta)/2=2`
or `(1+tan^(2) theta) (d theta)/2=2, or (1+4t^(2)) (d theta)/(dt)=2`
or `(d theta)/(dt)=2/(1+4t^(2)), (d theta)/(dt) at t=2s` is
`(d theta)/(dt)=2/(1+4(2)^(2))=2/17 rad//s`