Albert is piloting his spaceship, heading east with a speed of $0.90 \mathrm{c}$. Albert's ship sends a light beam in the forward (eastward) direction, which travels away from his ship at a speed $c$. Meanwhile, Isaac is piloting his ship in the westward direction, also at $0.90 c$, toward Albert's ship. With what speed does Isaac see Albert's light beam pass his ship?

You are in a spaceship, traveling directly away from the Moon with a speed of 0.9 c. A light signal is sent in your direction from the surface of the Moon. (a) As the signal passes your ship, do you measure its speed to be greater than, less than, or equal to 0.1 c? {b) Choose the best explanation from among the following: A. The speed you measure will be greater than 0.1 c; in fact, it will be c, since all observers in inertial frames measure the same speed of light B. You will measure a speed less than 0.1 c because light travels slower in the vacuum of space. C. You will measure a speed of 0.1 c, which is the difference between c and 0.9 c.

Suppose you fly on a rocket with a speed $v=0.99 \mathrm{c}$ for $1 \mathrm{y}$, according to the ship's clocks and calendars. How much time elapses on Earth during your $1 \mathrm{y}$ trip?

You are in a spaceship, traveling directly away from the Moon with a speed of $0.9 \mathrm{c}$. A light signal is sent in your direction from the surface of the Moon. As the signal passes your ship, do you measure its speed to be greater than, less than, or equal to $0.1 c$ ?

Choose the best explanation from among the following:

I. The speed you measure will be greater than $0.1 \mathrm{c}$; in fact, it will be $c$, since all observers in inertial frames measure the same speed of light. II. You will measure a speed less than $0.1 c$ because of time dilation, which causes clocks to run slow. III. When you measure the speed you will find it to be $0.1 c$, which is the difference between $c$ and $0.9 c$.

An x-ray beam of wavelength A undergoes first-order reflection (Bragg law diffraction) from a crystal when its angle of incidence to a crystal face is 23$^\circ$, and an x-ray beam of wavelength 97 pm undergoes third-order reflection when its angle of incidence to that face is 60$^\circ$. Assuming that the two beams reflect from the same family of reflecting planes, find the interplanar spacing.

You are in a spaceship, traveling directly away from the Moon with a speed of $0.9 \mathrm{c}$. A light signal is sent in your direction from the surface of the Moon. As the signal passes your ship, do you measure its speed to be greater than, less than, or equal to $0.1 c$ ?

You are in a spaceship, traveling directly away from the Moon with a speed of $0.9 \mathrm{c}$. A light signal is sent in your direction from the surface of the Moon. As the signal passes your ship, do you measure its speed to be greater than, less than, or equal to $0.1 c$ ?

During an auto accident, the vehicle's airbags deploy and slow down the passengers more gently than if they had hit the windshield or steering wheel. According to safety standards, airbags produce a maximum acceleration of 60g that lasts for only 36 ms (or less). How far (in meters) does a person travel in coining to a complete stop in 36 ms at a constant acceleration of 60g?

Two sources emit waves that are coherent, in phase, and have wavelengths of $26.0 \mathrm{~m}$. Do the waves interfere constructively or destructively at an observation point $44.0 \mathrm{~m}$ from one source and $135 \mathrm{~m}$ from the other source?

An astronaut travels to Mars with a speed of $8350 \mathrm{~m} / \mathrm{s}$. After a month $(30.0 \mathrm{~d})$ of travel, as measured by clocks on Earth, how much difference is there between the Earth clock and the spaceship clock? Give your answer in seconds.

A section of a sphere has a radius of curvature of $0.72 \mathrm{~m}$. If this section is painted with a reflective coating on both sides, what is the focal length of (a) the convex side and (b) the concave side?

A dentist's mirror is placed 2.0 cm from a tooth. The enlarged image is located 5.6 cm behind the mirror. (a) What kind of mirror (plane, concave, or convex) is being used? (b) Determine the focal length of the mirror. (c) What is the magnification? (d) How is the image oriented relative to the object?

Newly sprouted sunflowers can grow at the rate of $0.30 \mathrm{~in}$. per day. One such sunflower is left on Earth, and an identical one is placed on a spacecraft that is traveling away from Earth with a speed of $0.94 \mathrm{c}$. How tall is the sunflower on the spacecraft when a person on Earth says his is $2.0 \mathrm{~in}$. high?

An astronaut moving with a speed of $0.65 \mathrm{c}$ relative to Earth measures her heart rate to be $72$ beats per minute. Calculate the astronaut's heart rate as measured on Earth.