In the preceding exercise, if the stick is moving in a direction along its length (like a properly thrown spear), how long will you measure its length to be?

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?

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

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?

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?

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

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.

If you were on Earth monitoring a person in a rocket ship traveling away from Earth at a speed close to the speed of light, what changes would you note in his pulse? In his volume? Explain.