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Chapter 1: Problem 37
How many millimeters in a kilometer?
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A football field's length is exactly 100 yards, and its width is \(53 \frac{1}{3}\) yards. A quarterback stands at the exact center of the field and throws a pass to a receiver standing at one corner of the field. Let the origin of coordinates be at the center of the football field and the \(x\) -axis point along the longer side of the field, with the \(y\) -direction parallel to the shorter side of the field. a) Write the direction and length of a vector pointing from the quarterback to the receiver. b) Consider the other three possibilities for the location of the receiver at corners of the field. Repeat part (a) for each.
A tank is in the shape of an inverted cone, having height \(h=2.5 \mathrm{~m}\) and base radius \(r=0.75 \mathrm{~m} .\) If water is poured into the tank at a rate of \(15 \mathrm{~L} / \mathrm{s}\), how long will it take to fill the tank?
The distance from the center of the Moon to the center of the Earth ranges from approximately \(356,000 \mathrm{~km}\) to \(407,000 \mathrm{~km}\). What are these distances in miles? Be certain to round your answers to the appropriate number of significant figures.
For the planet Mars, calculate the distance around the Equator, the surface area, and the volume. The radius of Mars is \(3.39 \cdot 10^{6} \mathrm{~m}\)
How many significant figures are in each of the following numbers? a) 4.01 c) 4 e) 0.00001 g) \(7.01 \cdot 3.1415\) b) 4.010 d) 2.00001 f) \(2.1-1.10042\)
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