Homework

Back to serious stuff. On number 9, remembering your calculus is a big help. For instance, note

\frac{dv_x^{\prime}}{dt^{\prime}} = \frac{dv_x^{\prime}/dt}{dt^{\prime}/dt}

and use the Lorentz transformations along with velocity addition. I'll spell this out more tomorrow in recitation.

For number 6, the x component of the velocity is just what you think it is. However: the y component of the velocity in the second reference frame would be

u_y^{\prime}=\frac{dy^{\prime}}{dt^{\prime}}

Since

y=y^{\prime}

the numerator is trivial. However, there is still time dilation, so you'll need to use the Lorentz transformation to relate dt and dt'. Again, remember the calculus trick above, and the main point is this: the velocity along the direction of relative motion follows the addition formula we derived, but along the orthogonal direction, there is still a transformation because while distance is uncontracted, time is still dilated.

We'll go over the rest tomorrow, but you will find many of the other questions in my PH102 notes or previous PH102 homework sets. I'll give some hints on where to look ... but start with the problems at the end of Ch. 1.