Two atomic clocks are carefully synchronized. One remains in New York, and the other is loaded on an airliner that travels at an average speed of 250 m/s and then returns to New York. When the plane returns, the elapsed time on the clock that stayed behind is 4.00 h. By how much will the readings of the two clocks differ, and which clock will show the shorter elapsed time?

Answer the question below by reading the most recent consolidated financial statements of the American Red Cross (ARC) at its website, www.redcross.org. (The financial statements may be accessed through the Publications link on the website's home page.)

• Assume the ARC received a cash contribution during the most recent year that the donor restricted for disaster relief. Also assume that the ARC spent the amount donated in the year for disaster relief. Specify whether the ARC would report this donation on its statement of activities for the most recent year as (1) an increase in net assets without donor restrictions when the donation was received or (2) an increase in net assets with donor restrictions when the donation was received and as a reclassification of net assets from "with donor restrictions" to "without donor restrictions" when the donation was used.

Two atomic clocks are carefully synchronized. One remains in New York, and the other is loaded on an airliner that travels at an average speed of $250 \mathrm{~m} / \mathrm{s}$ and then returns to New York. When the plane returns, the elapsed time on the clock that stayed behind is $4.00 \mathrm{~h}$. By how much will the reading of the two clocks differ, and which clock will show the shorter elapsed time? (Hint; Since $u \ll c$, you can simplify $\sqrt{1-u^2 / c^2}$ by a binomial expansion.)

Two identical clocks are synchronized. One is then put in orbit directed eastward around the Earth while the other remains on the Earth. Which clock runs slower? When the moving clock returns to the Earth, are the two still synchronized?

A spacecraft flies away from the earth with a speed of $4.80 \times 10^{6} \mathrm{m} / \mathrm{s}$ relative to the earth and then returns at the same speed. The spacecraft carries an atomic clock that has been carefully synchronized with an identical clock that remains at rest on earth. The spacecraft returns to its starting point 365 days (1 year) later, as measured by the clock that remained on earth. What is the difference in the elapsed times on the two clocks, measured in hours? Which clock, the one in the spacecraft or the one on earth, shows the shorter elapsed time?

Write the equation in exponential form.

$$\log _ { 2 } 1024 = 10$$

Find the root of the equation.

$$\frac{3}{5}x - {1}{2} = 0$$

How much work must be done on a particle with mass m to accelerate it from a speed of 0.900c to a speed of 0.990c? (Express the answers in terms of $mc^{2}$.)

Two identically constructed clocks are synchronized. One is put in an eastward orbit around Earth while the other remains on Earth. Which clock runs slower? When the moving clock returns to Earth, will the two clocks still be synchronized?

A spaceship moving $0.80 \: \mathrm{c}$ direction away from Earth fires a missile that the spaceship measures to be moving at $0.80 \: \mathrm{c}$ perpendicular to the ship's direction of travel. Find the velocity components and speed of the missile as measured by Earth.

How much work must be done on a particle with mass m to accelerate it from rest to a speed of 0.090c ? (Express the answers in terms of $mc^{2}$.)

Is it possible to synchronize clocks that are in motion relative to each other? Try to design a method to do so. Which observers will believe the clocks to be synchronized?

A space probe is sent to the vicinity of the star Capella, which is 42.2 light-years from the earth. (A light-year is the distance light travels in a year.) The probe travels with a speed of 0.9930c. An astronaut recruit on board is 19 years old when the probe leaves the earth. What is her biological age when the probe reaches Capella?

An astronaut is traveling in a space vehicle that has a speed of 0.500c relative to Earth. The astronaut measures his pulse rate at 75.0 per minute. Signals generated by the astronaut’s pulse are radioed to Earth when the vehicle is moving perpendicular to a line that connects the vehicle with an Earth observer. (a) What pulse rate does the Earth observer measure? (b) What would be the pulse rate if the speed of the space vehicle were increased to 0.990c?