If a high-speed spaceship appears shrunken to half its normal length, how does its momentum compare with the classical formula $p=m v$ ?

A person riding on the roof of a freight train throws a ball forward. (a) If we ignore air drag and relative to the ground, is the ball moving faster or slower when the train is moving than when it is standing still? (b) Relative to the freight car, is the ball moving faster or slower when the train is moving than when the train is standing still?

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

The formula that relates the speed, frequency, and wavelength of electromagnetic waves, $v=f \lambda$, was known before relativity was developed. Relativity has not changed this equation, but it has added a new feature to it. What is that feature?

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?

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

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 $c$.

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?

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

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.

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?

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?

Do the relativity equations for time, length, and momentum hold true for everyday speeds? Explain.