Mistake in Exercises for the Feynman Lectures?

[suh112]

Homework Statement

This is problem 14.1 from "Exercises for the Feynman Lectures on Physics":

14.1 A rigid wheel of radius R is rolling without slipping on a horizontal surface. The plane of the wheel is vertical, and the axis of the wheel is moving horizontally with a speed V relative to the surface. If the axis of the wheel is parallel to the z-axis, V is in the positive x-direction, and $\theta$ the angle through which the wheel has rotated since a certain point P on the rim was in contact with the ground, show that the instantaneous velocity (speed and direction) of the point P is given by
v = V ((1- cos$\theta$)i + (sin $\theta$) j).

Relevant Equations

v = V ((1- cos$\theta$)i + (sin $\theta$) j)

It seems to me that the answer should be v = V((1+sinθ)i -(cosθ)j) intuitively since $V_x$ should be zero at θ = −π\2 and should be greatest when the angle is 90 degrees. Similarly, the component of velocity in the y direction should be greatest when the angle $\theta$ is 180 degrees and zero when $\theta$ is 0 degrees. Am I doing something wrong?

 

[kuruman]

According to the statement of the question, angle θ is "the angle through which the wheel has rotated since a certain point P on the rim was in contact with the ground". If the wheel rolls without slipping what is the speed of certain point P on the rim relative to the point of contact with the ground? Does the given expression predict that? Does your expression predict that?

 

[suh112]

According to the statement of the question, angle θ is "the angle through which the wheel has rotated since a certain point P on the rim was in contact with the ground". If the wheel rolls without slipping what is the speed of certain point P on the rim relative to the point of contact with the ground? Does the given expression predict that? Does your expression predict that?

Oh I misread the question. This makes sense thanks.