Chapter 33, Problem 70P

Equation 33.5a transforms the velocity $\stackrel{\to }{u}$ of an object moving in the x-direction—the same direction as the relative velocity $\stackrel{\to }{v}$ of the two reference frames. Now suppose the object’s velocity also has a component u_y perpendicular to the two frames’ relative velocity $\stackrel{\to }{v}$. Find the transformation from ${u^{\prime }}_y$ to u_y.