Answer:
[tex]\theta=\frac{\pi}{4}+2\frac{rad}{s}t[/tex]
Explanation:
To find the expression in terms of time t you take into account the following equation for the angular distance traveled by an object with angular acceleration w and initial angular position θo:
[tex]\theta=\theta_o+\omega t+\frac{1}{2}\alpha t^2[/tex] Â ( 1 )
α is the angular acceleration, but in this case you have a circular motion with constant angular speed, then α = 0 rad/s^2. θo is the initial angular position, the information of the question establishes that Enrique is at 3-o'clock. This position can be taken, in radian, as π/4 (for 12-o'clock = 0 rads).
The angular speed is:
[tex]\omega=2\frac{rad}{min}[/tex]
You replace the values of θo, α and w in the equation ( 1 ):
[tex]\theta=\frac{\pi}{4}+2\frac{rad}{s}t[/tex]
Furthermore, the arc length is:
[tex]s=r\theta=(40ft)[\frac{\pi}{4}+2\frac{rad}{s}t][/tex]
