When observed from the sun at a particular instant, Earth and Mars appear to move in opposite directions with speeds 108,000 km/h and 86,871 km/h, respectively. What is the speed of Mars at this instant when observed from Earth?

When a missile is shot from one spaceship towards another, it leaves the first at 0.950c and approaches the other at 0.750c. What is the relative velocity of the two ships?

A man is running on a straight road perpendicular to a train track and away from the track at a speed of 12 m/ s. The train is moving with a speed of 30 m/s with respect to the track. What is the speed of the man with respect to a passenger sitting at rest in the train?

A highway patrol officer uses a device that measures the speed of vehicles by bouncing radar off them and measuring the Doppler shift. The outgoing radar has a frequency of 100 GHz and the returning echo has a frequency 15.0 kHz higher. What is the velocity of the vehicle? Note that there are two Doppler shifts in echoes. Be certain not to round off until the end of the problem, because the effect is small.

The speed of light is 3 $\times$ 10$^8$ m/s and the distance from Earth to the sun is 1.5 $\times$ 10$^{11}$ m. How many seconds does it take for sunlight to reach Earth? Write your answer in scientific notation.

Mr. Walker drove 20 miles to pick up supplies for the Science Olympiad. If the trip to the supply store took 0.75 hours, what was his unit speed for one hour?

Think of an experiment you did in a past science class. a. Describe the experiment. b. What was the experimental variable? c. What were two control variables? d. What was the outcome of the experiment?

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.

The Sun is approximately $1.44 \times 10^{11}$ meters from Earth. If light travels $3 \times 10^8$ meters per second, how many minutes does it take light from the sun to reach Earth?

Solve. Write the answer in scientific notation.

The mass of Earth is $5.9 \times 10^{24} \mathrm{~kg}$. The mass of the sun is $2 \times 10^{30} \mathrm{~kg}$. How many times heavier is the sun than Earth?

The gravitational attraction of the Sun and the Moon on the Earth produces tides. The Sun’s tidal effect is about half as great as the Moon’s. The direct pull of the Sun on the Earth, however, is about $175$ times that of the Moon. Why is it then that the Moon causes the larger tides?

A rocket is headed away from Earth at a speed of $0.80 c$. The rocket fires a smal payload at a speed of $0.70 c$ (relative to the rocket) aimed away from Earth. How fast is the payload moving relative to Earth? $(a)$ $1.50 \mathrm{c}$, $(b)$ a little less than $1.50 c$. $(c)$ a little over $c$. $(d)$ a little under $c$. $(e)$ $0.75 c$.

What is the definition of an astronomical unit? A. the average distance from Jupiter to the Sun B. the average distance from Earth to the Moon C. the average distance from Earth to the Sun D. the average distance from the Sun to the next nearest star.

A muon formed high in Earth’s atmosphere travels toward Earth at a speed v = 0.990c for a distance of 4.60 km as measured by an observer at rest with respect to Earth. It then decays into an electron, a neutrino, and an antineutrino. A third observer traveling toward the muon at c/2 measures the lifetime of the particle. According to this observer, is the muon’s lifetime shorter or longer than the lifetime measured by the observer at rest with respect to Earth? Explain.