The bus in the preceding problems is 70 feet long, according to its passengers and driver. Show that its length is seen as slightly less than 10 feet from a vantage point on a fixed planet.

A starship passes Earth at $80 \%$ of the speed of light and sends a drone ship forward at half the speed of light relative to itself. Show that the drone travels at $93 \%$ of the speed of light relative to Earth.

The isotope cesium-$137$, which has a half-life of $30$ years, is a product of nuclear power plants. How long will it take for this isotope to decay to about one-half its original amount? (a) $0 \mathrm{yr}$ (b) $15 \mathrm{yr}$ $(c)$ $30 \mathrm{yr}$ (d) $60 \mathrm{yr}$ (e) $90 \mathrm{yr}$

A simple ideal Brayton cycle with air as the working fluid has a pressure ratio of 10. The air enters the compressor at 520 R and the turbine at 2000 R. Accounting for the variation of specific heats with temperature, determine (a) the air temperature at the compressor exit, (b) the back work ratio, and (c) the thermal efficiency.

An air-standard Diesel cycle has a compression ratio of 16 and a cutoff ratio of 2. At the beginning of the compression process, air is at 95 kPa and $27^{\circ} \mathrm{C}.$ Accounting for the variation of specific heats with temperature, determine (a) the temperature after the heal-addition process, (b) the thermal efficiency, and (c) the mean effective pressure.

A cylinder contains $0.0100$ mol of helium at $T=27.0\degree \mathrm{C}$.
(b) If instead the pressure of the helium is kept constant, how much heat is needed to raise the temperature from $27.0\degree \mathrm{C}$ to $67.0\degree \mathrm{C}$? Draw a $p V$-diagram for this process.

According to Newtonian mechanics, the momentum of the bus in the preceding problem is $p=m v$. According to relativity, it is $p=\gamma$. How does the actual momentum of the bus moving at $0.99 c$ compare with the momentum it would have if classical mechanics were valid? How does the momentum of an electron traveling at $0.99 c$ compare with its classical momentum?

A spaceship is moving with a speed of $v=0.99 c$. A passenger in the spaceship heats her food for 2 minutes according to her watch. Calculate the duration of heating as observed from a fixed planet.

A spaceship is moving with a speed of $v=0.99 c$. A passenger in the spaceship heats her food for 2 minutes according to her watch. Calculate the duration of heating as observed from a fixed planet.

What classical idea about space and time did Einstein reject?

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 $c$.

(El /la más). El almacén Velasco es buenísimo, ¿no? (centro comercial)

A team of engineering students is designing a catapult to launch a small ball at A so that it lands in the box. If it is known that the initial velocity vector makes a 300 angle with the horizontal, determine the range of launch speeds $v_{0}$ for which the ball will land inside the box.

A 120 -volt ac source powers the circuit shown. How many volts are impressed across the lightbulb, and how many amps flow through it?