If stationary observers measure the shape of a passing object to be exactly circular, what is the shape of the object when viewed face-on by observers on board the object, traveling with it?

A passenger on an interplanetary express bus traveling at $v=0.10 c$ takes a $5$-minute catnap, according to her watch. Show that her catnap from the vantage point of a fixed planet lasts slightly more than $5$ minutes.

Pretend that the starship in the preceding problem is somehow traveling at $c$ with respect to Earth and it fires a drone forward at speed $c$ with respect to itself. Use the equation for the relativistic addition of velocities to show that the speed of the drone with respect to Earth is still $c$.

You decide to roll a 0.1-kg ball across the floor so slowly that it will have a small momentum and a large de Broglie wavelength. If you roll it at $0.001 \mathrm{~m} / \mathrm{s}$, what is its wavelength? How does this compare with the de Broglie wavelength of the high-speed electron in the previous problem?

An object is moving vertically, will any contraction take place in a horizontal direction?

Pretend that the starship Enterprise in the previous problem is somehow traveling at $c$ with respect to the Earth, and it fires a drone forward at speed $c$ with respect to itself. Use the equation for the relativistic addition of velocities to show that the speed of the drone with respect to the Earth is still $c$.

How do the measured densities of a body compare at rest and in motion?

What classical idea about space and time did Einstein reject?

If you lived in a world where people regularly traveled at speeds near the speed of light, why would it be risky to make a dental appointment for $10: 00 \mathrm{AM}$ next Thursday?

At $6.00$ AM a hospital uses its cyclotron to make 1 milligram of the isotope fluorine- 18 for use as a diagnostic tool with its PET scanner. The half-life of F-18 is $1.8$ hours. How much $\mathrm{F}-18$ is left ar 3:00 PM? At midnight? Should the hospital plan to make more F-18 the next morning?

Does the equation for time dilation show dilation occurring for all speeds, whether slow or fast? Explain.

Because of time dilation, you observe the hands of your friend's watch to be moving slowly. How does your friend view your watch: as running slowly, running rapidly, or neither?

An astronaut is travelling in space at speeds close to the speed of light. Compare the time being spent in space by the astronaut with the time elapsing on Earth.

Due to length contraction, you see people in a spaceship passing by you as being slightly narrower than they normally appear. How do these people view you?