University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 1 - Units, Physical Quantities, and Vectors - Problems - Exercises: 1.3

Answer

1.02 ns

Work Step by Step

For this question, we need to use the speed of light in a vacuum, approximately 3.0 x 10^8 m/s. The initial quantity is given in feet, so for our conversion factor to be useful, we must first convert feet to meters. The easiest way to do this would be feet to inches (12 inches = 1 foot), then inches to centimeters (2.54 cm = 1 in), then centimeters to meters (100 cm = 1 m). Then we can multiply by the inverse of the speed of light to give us an answer in seconds. Then we need to convert seconds to nanoseconds at 10^9 ns = 1 s. Strung together we get: 1.00 ft x (12 in/ft) x (2.54 cm/in) x (m/100 cm) x (1/3x10^8 s/m) x (10^9 ns/s) = 1.016 ns Don't forget to cancel units that show up on the top and bottom of the formula! Ft, in, cm, m, and s cancel, leaving us with units of ns, which is what we want. Our answer should have the same number of significant figures as the initial quantity. 1.00 ft has 3 sig figs, so we should round our answer to 1.02 ns.
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