Explanation
The distance d travelled by point P after a revolution by an angle θ is given by the length of the arc travelled by point P. This distance is given by:
[tex]\text{ distance }=\text{ arc length }=r\timesθ.[/tex]
Where r is the radius of the circle and θ is the angle of the revolution in radians.
Now, in this case, we have r = 1 foot. Replacing this value in the equation above, we get:
[tex]\text{ distance }=(1\text{ ft})\timesθ=θ\text{ ft.}[/tex]
So we see that the distance travelled (in ft) by the point P is just the magnitude of the angle θ (in radians).
Answer
The distance travelled by point P is given by the length of arc travelled, which is given by:
[tex]\text{ distance }=\text{ arc length =}r\timesθ=\text{ 1 ft}\times\text{ }θ\text{ }=θ\text{ ft.}[/tex]
