iii) The well is in fact 78 m deep. Take g = 9.8 ms-2and calculate T1iv) On the same displacement-time graph, show the displacement of the sound wave pulse that travels from the bottom to the top of the well. Your graph need not be to scale. v) Taking the speed of sound to be 344 ms-1, calculate T2, the time taken for the sound to travel from the bottom of the well to reach the scientist at the top. Show T2on your graph. vi) State the time T between release of the stone and arrival of the sound. Think carefully about the number of significant figures. . . vii) What value does the scientist get for the depth of the well? viii) Comment on the relative size of the errors involved in (a) neglecting the time of travel of sound, (b) approximating the value of g and (c) measurement error. Vectors and Relative Motion 4. A person going for a walk follows the path shown in the diagram. Taking the starting point as the origin and using 𝚤𝚤̂, 𝚥𝚥̂, 𝑘𝑘�notation (a) write a vector displacement for each straight line segment of the walk. (b) determine the person's resultant vector displacement at the end of the walk. (c) determine the distance and direction of the end point from the start point. � 6. A person, travelling eastward at the rate of 4.0 km hr–1, observes that the wind seems to blow directly from the north; on doubling his speed the wind appears to come from the northeast; determine the direction of the wind and its velocity. 200 m60°100 mEnd 𝑥𝑥𝑦𝑦30°300 m
9 7. A rower wishes to cross a rapidly flowing river of width 40 m, which is flowing uniformly at a rate of 5.0 ms–1. The rower starts at point A and heads in a direction θ, as shown, rowing at a speed of 2.0 ms–1relative to the water. (a) Write down an expression for the velocity of the rower relative to the river bank, in terms of unit vectors 𝚤𝚤̂and 𝚥𝚥̂(b) Write down the displacement of the rower at time t. (c) If the rower wishes to cross the river in minimum time, in what direction should she head? What is the crossing time and how far from point B will she land? (d) If the rower wishes to land as close to B as possible, in what direction should she head? What will be the crossing time and distance of landing point from B in this case? Hint: what technique do you use to find the minimum of a function? . Motion in Two and Three Dimensions
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