How Many Drops in All the Oceans? Part A How many drops of water are in all the oceans on earth? Assume that contains 25 drops of water. Remember that this is an order-of-magnitude problem, so you should expect that you will only find rough estimates for the numbers you require. Hint A.1 Mean depth of the oceans The mean (average) depth of the oceans is about . Hint A.2 Radius of the earth The radius of the earth is about . Hint A.3 Percent of the earth covered by ocean About 70% of the earth is covered by oceans. Hint A.4 Surface area of a sphere The surface area of a sphere with radius is given by the formula . Express your answer to one significant figure. ANSWER: 4.0×10 25 Correct drops Although order-of-magnitude calculations may seem silly at times, they are a major tool used by physicists. Any time that you are solving a problem in physics, it is helpful to have an estimate in your head of the order of magnitude that you expect from the answer. For instance, if you were trying to find the average speed of a car over a long trip and got an answer of 1000 miles per hour, you would immediately know that you had done something wrong, because your answer has the wrong order of magnitude. Order-of-magnitude problems are sometimes called Fermi problems, after the physicist Enrico Fermi who was reportedly a master of such approximate calculations. When the first atomic bomb was tested, Fermi was able to get a rough estimate of the power that the bomb released by throwing some torn bits of paper into the air as the pressure wave from the bomb passed him and then performing a rough calculation. Tracking a Plane A radar station, located at the origin of xz plane, as shown in the figure
station from the east. At first observation (point A), the position of the airplane relative to the origin is . The position vector has a magnitude of 360 and is located at exactly 40 above the horizon. The airplane is tracked for another 123 in the vertical east-west plane for 5.0 , until it has passed directly over the station and reached point B. The position of point B relative to the origin is (the magnitude of is 880 ). The contact points are shown in the diagram, where the x axis represents the ground and the positive z direction is upward. Part A Define the displacement of the airplane while the radar was tracking it: . What are the components of ? Hint A.1 How to approach the problem Keep in mind that .According to the rules of vector addition and subtraction, the x component of is . Hint A.2 Finding the components of What are the components of in the and directions? Express your answer in meters as an ordered pair, separating the x and z values with commas, to three significant figures. ANSWER:
This is the end of the preview. Sign up to
access the rest of the document.