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HW1ans - Physics 112 HW#1 Solutions 1450 mi/h 1.609 km 1 mi...

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Physics 112 - HW #1 Solutions 1-7 (a) 1450 mi/h 1.609 km 1 mi = 2330 km/hr (b) 2330 km/hr 10 3 m 1 km 1 hr 3600 s = 648 m/s 1-12 1 yr = 1 yr 365.24 days yr 24 hr day 3600 s hr = 3.156 × 10 7 s π = 3.1416 fractional error = 3 1557 10 3 1416 10 3 1557 10 7 7 7 . . . × × × s s s = 0.00447 = 0.447% 3 significant digits! [NOTE: Our calculation starts with 5 significant digits since that’s the number of significant digits given in 1 yr = 365.24 days. The conversion factors, 1 day = 24 hr and 1 hr = 3600 s, are regarded as exact , i.e., definitions without uncertainty.] 1-26 Estimates : Oceans cover about 70% = 0.7 of the Earth. Average depth of the oceans ~ 2.5 miles ~ 4000 m 1 drop ~ 0.05 mL (milliliter) = 0.05 (10 -3 × 10 -3 m 3 ) = 5 × 10 -8 m 3 (i.e., roughly 20-25 drops/mL) Radius of the Earth R = 6.4 × 10 6 m Area of the Earth = 4 π R 2 = 4 π (6.4 × 10 6 m) 2 ~ 5 × 10 14 m 2 Area of the oceans ~ 0.7 (5 × 10 14 m 2 ) ~ 3.5 × 10 14 m 2 Volume of oceans = avg. depth × area = (4000 m)( 3.5 × 10 14 m 2 ) ~ 1.4 × 10 18 m 3 # drops in the oceans ~ 1.4 × 10 18 m 2 5 × 10 -8 m 3 ~ 3 × 10 25 or ~ 10 25
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