position of the peg is given by the equation
[tex]r = 4 sin2\theta[/tex]
now the rate of change in position is given as
[tex]v = \frac{dr}{dt}[/tex]
[tex]v = \frac{d}{dt}(4 sin2\theta)[/tex]
[tex]v = 8cos2\theta*\frac{d\theta}{dt}[/tex]
[tex]v = 8 cos2\theta*\omega[/tex]
given that
[tex]\omega = 1 rad/s[/tex]
[tex]\theta = 59 degree[/tex]
now we have
[tex]v = 8*cos(2*59)* 1 = -3.76 m/s[/tex]
so its speed will be 3.76 m/s in magnitude
