A spaceship travels at a constant speed from earth to a planet orbiting another star. When the spacecraft arrives, 12 years have elapsed on earth, and 9.2 years have elapsed on board the ship. How far away (in meters ) is the planet, according to observers on earth?

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.990 c, and an observer who is stationary in a laboratory measures the pion's lifetime to be

$$3.5 \times 10 ^ { - 8 } \mathrm { s }$$

(a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart?

The dissociation energy of a molecule is the energy required to break apart the molecule into its separate atoms. The dissociation energy for the cyanogen molecule is $1.22 \times 10 ^ { - 18 } \mathrm { J }$ Suppose that this energy is provided by a single photon. Determine the

wavelength and

frequency of the photon.

Suppose the straight-line distance between New York and San Francisco is $4.1 \times 10^{6} \mathrm{m}$ (neglecting the curvature of the earth). A UFO is flying between these two cities at a speed of 0.70 c relative to the earth. What do the voyagers aboard the UFO measure for this earth. What do the voyagers aboard the UFO measure for this distance?

A high-orbiting spaceship travels at $7 \mathrm{~km} / \mathrm{s}$ with respect to Earth. Suppose it projects a capsule rearward at $7 \mathrm{~km} / \mathrm{s}$ with respect to the ship. Describe the path of the capsule with respect to Earth.

A laser emits

$$1.30 \times 10 ^ { 18 }$$

photons per second in a beam of light that has a diameter of 2.00 mm and a wavelength of 514.5 nm. Determine (a) the average electric field strength and (b) the average magnetic field strength for the electromagnetic wave that constitutes the beam.

A proton is located at a distance of 0.420 m from a point charge of

$$+ 8.30 \mu \mathrm { C }$$

The repulsive electric force moves the proton until it is at a distance of 1.58 m from the charge. Suppose that the electric potential energy lost by the system is carried off by a photon that is emitted during the process. What is its wavelength?

The distance from earth to the center of our galaxy is about 23 000 ly (1 ly=1 light-year=$9.47 \times 10^{15} \mathrm{m} )$, as measured by an earth-based observer. A spaceship is to make this journey at a speed of 0.9990c. According to a clock on board the spaceship, how long will it take to make the trip? Express your answer in years (1 yr=$3.16 \times 10^{7} \mathrm{s} )$.

An AM radio station broadcasts an electromagnetic wave with a frequency of 665 kHz, whereas an FM station broadcasts an electromagnetic wave with a frequency of 91.9 MHz. How many AM photons are needed to have a total energy equal to that of one FM photon?

Consider a person along with a frame of reference in each of the following situations. In which one or more of the following situations is the frame of reference an inertial frame of reference? (a) The person is oscillating in of reference an inertial frame of reference? (a) The person is oscillating in a simple harmonic motion at the end of a bungee cord. (b) The person is in a car going around a circular curve at a constant speed. (c) The person is in a plane that is landing on an aircraft carrier. (d) The person is in the space shuttle during lift-off. (e) None of the above.

The nucleus of the hydrogen atom has a radius of about

$$1 \times 10 ^ { - 15 } \mathrm { m }$$

The electron is normally at a distance of about

$$5.3 \times 10 ^ { - 11 } \mathrm { m }$$

from the nucleus. Assuming the hydrogen atom is a sphere with a radius of

$$5.3 \times 10 ^ { - 11 } \mathrm { m }$$

find (a) the volume of the atom, (b) the volume of the nucleus , and (c) the percentage of the volume of the atom that is occupied by the nucleus.

Suppose that you are using a microscope to view two closely spaced cells. For a given lens diameter, which color of light would you use to achieve the best possible resolving power? (a) Red, (b) Yellow, (c) Green, (d) Blue, (e) All the colors give the same resolving power.

A spaceship is traveling away from Earth at 0.87c. The astronauts report home by radio every 12 h (by their own clocks). At what interval are the reports sent to Earth, according to Earth clocks?

Two spaceships A and B are exploring a new planet. Relative to this planet, spaceship A has a speed of 0.60c, and spaceship B has a speed of 0.80c. What is the ratio

$$D _ { A } / D _ { \mathrm { B } }$$

of the values for the planet's diameter that each spaceship measures in a direction that is parallel to its motion?