(II) Determine the conversion factor between (a) km/h and mi/h,(b) m/s and ft/s,(c) km/h and m/s.

(II) (a) How many seconds are there in 1.00 year? (b) How many nanoseconds are there in 1.00 year? (c) How many years are there in 1.00 second?

(II) A light-year is the distance light travels in one year (at speed there in 1.00 light-year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth, 1.50 X 10° km. How many AU are there in 1.00 light-year? (c) What is the speed of light in AU/h? 2.998 × 10° m/s). (a) How many meters are 1. :(2.998 x 1o m)co0) c 60) C24) C365) 9.454x1015 m 265 X 24 x 62 X 6 0 (9.454 150X do

(III) The smallest meaningful measure of length is called the Planck length, and is defined in terms of three fundamental constants in nature: the speed of light c the gravitational constant G = 6.67 × 10-11 m³/kg•s², and Planck's constant h = 6.63 × 10-34 kg·m²/s. The Planck length {p is given by the following combination of these three constants: 3.00 × 10° m/s, Gh lp Show that the dimensions of lp are length [L], and find the order of magnitude of lp. [Recent theories (Chapters 32 and 33) suggest that the smallest particles (quarks, leptons) are “strings" with lengths on the order of the Planck length, 10-35 m. These theories also suggest that the “Big Bang," with which the universe is believed to have begun, started from an initial size on the order of the Planck length.]

Hold a pencil in front of your eye at a position where its blunt end just blocks out the Moon (Fig. 1–19). Make appropriate measurements to estimate the diameter of the Moon, given that the Earth-Moon distance is 3.8 × 10° km. FIGURE 1-19 Problem 48. How big is the Moon?

(II) A light-year is the distance light travels in one year (at speed = 2.998 × 10° m/s). (a) How many meters are there in 1.00 light-year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth, 1.50 x 10 km. How many AU are there in 1.00 light-year? (c) What is the speed of light in AU/h?

(II) A light-year is the distance light travels in one year (at speed =2.998 x 108 m/s). (a) How many meters are there in 1.00 light-year? (b) An astronomical unit (AU) is the average distance from the Sun to Earth, 1.50 x 108 km. How many AU are there in 1.00 light-year?

The average distance between Earth and the Sun is 1.5 × 1011 m. (a) Calculate the average speed of Earth in its orbit (assumed to be circular) in meters per second. (b) What is this speed in miles per hour?

(III) I agree to hire you for 30 days. You can decide between two methods of payment: either (1) $1000 a day, or (2) one penny on the first day, two pennies on the second day and continue to double your daily pay each day up to day 30.Use quick estimation to make your decision, and justify it.