A rocket cruises past a laboratory at 1.00×10⁶ m/s in the positive x-direction just as a proton is launched with velocity (in the laboratory frame) $\vec{v}=(1.41\times {10}^6\hat{i}+1.41\times {10}^6\hat{j})$ m/s. What are the proton's speed and its angle from the y-axis in the rocket frame?

A rocket zooms past the earth at v=2.0×10⁶ m/s. Scientists on the rocket have created the electric and magnetic fields shown in FIGURE EX31.4. What are the fields measured by an earthbound scientist?