Question: There are 1.61 kilometers in a mile. How many kilometers are there in 10 miles?
Answer: 1.61 km x 10 = 16.1 km.
Question: There are 5.878 x 1012 miles in a light year. How many miles are there in 13 light-years? (if your answer is 1.23 x 104, you should enter it as 1.23e4)
Answer: 13 x 5.878e12 miles = 7.64e13 miles.
Question: Highway speed is about 100 km/hour. Suppose you could drive a car at this speed to the planet Venus when it is 0.28 AU away from us. How many hours would it take to get there? (1 AU is 150 million kilometers.)
Answer: The distance to drive is 0.28 AU = 0.28 x 150e6 km = 4.2e7 km. Time it takes to drive is the distance divided by the speed, so the answer in hours should be (4.2e7)/(100)=4.2e5 hours (or about 4800 years)
Question: The radius of the Earth is about 6,400 km. If you say "hello" to your friend Joe on the other side of the Earth via a satellite phone, how long will that message to take to reach Joe if the message travels at the speed of light?
Answer: Your cell phone reception is sure to be bad in the center of the Earth because light does not travel well through rocks and bricks. Your phone call to Joe will thus have to travel along the surface of the Earth, and that distance is pi (3.14) times radius or 3.14 x 6400 km = 20096 km. Speed of light is about 300,000 km/second. Again, the time it takes for light to travel to Joe is the distance divided by the speed (just like driving). So the time it takes the message to travel is (distance)/(speed) = 20096 km / 3e5 km/second = 0.067 second. That's about the time it takes you to blink.
Question: Your friend Joe is now sitting on the Moon. If you say "hello" to Joe using a radio from Houston, how long will that message to take to reach Joe if the message travels at the speed of light?
Answer: This is the same question as Q5, but the distance is now changed to the distance to the Moon. On page A-2 of your textbook, you should find that the average distance to the Moon is 384.4e3 km. Speed of light is about 3e5 km/second. Then the time it takes for light to travel to Joe is the distance divided by speed, i.e., (distance)/(speed) = 384.4e3 km / 3e5 km/second = 1.3 second. That's about one tick of your clock.
Question: Now Joe is inside a spaceship orbiting the Sun. If you say "hello" to Joe using a radio from Houston, how long will that message to take to reach Joe if the message travels at the speed of light?
Answer: This is the same question as Q6, but the distance is now changed to the distance to the Sun. You should find in your textbook that the average distance to the Sun is about 1.5e8 km. Speed of light is about 3e5 km/second. So, the time it takes for light to travel to Joe is the distance divided by speed, i.e., (distance)/(speed) = 1.5e8 km / 3e5 km/second = 500 seconds. That's about 8 minutes 20 seconds! So, the next time Tom Hanks (Liv Tyler?) says "Houston, we have a problem here", in his next movie spaceship exploring the Sun, the moviegoers will have to twiddle their thumbs for about 8 minutes before you get to say, "What?"
Question:If Polaris is 40 degrees from your zenith, what is your latitude?
Answer:You can see in the textbook that latitude (LA) and the zenith angle (ZA) of Polaris are related as "ZA = 90 - LA" or "LA = 90 - ZA". So at the North Pole, Polaris is directly overhead (ZA = 0), and your latitude LA = 90 - 0 = 90 degrees. If ZA = 40 as in this question, then your LA = 90 - 40 = 50 degrees.