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Unformatted text preview: Word Problems and Qualitative Conceptual Problems 1. A plane can fly at 180 km/h in still air. The plane attempts to head North, but after 30 minutes the plane has actually travelled 80 km at an angle 5 ◦ East of North. What is the wind velocity and in what direction should the pilot have headed to reach the intended destination? 2. Describe the set of points Q such that ~ P Q × B = ~ 0. 3. A ball rolls off a table with a speed of 2 feet per second. The table is 3.5 feet high. At what angle does the ball hit the floor? 4. How fast do you have to hit a baseball to clear a 30 foot fence that’s 400 feet away, assuming the baseball is 2 feet off the ground when you hit it (ignore air resistance)? 5. A transfer curve between two straight segments of train track is a connecting curve which makes the slope continuous and the curvature continuous (so there is no sudden change of acceleration). Find a polynomial y = P ( x ) transfer curve between the negative xaxis and the digaonal y = x , for x ≥ 1. 6. A bug crawls at speed 1 inch per second out from the center of a merry go round spinning at 1 revolution per second. At what point is the bug’s normal acceleration equal to its tangential acceleration? 1 7. Which of these functions, expressed in polar coordinates, are continuous at the origin? (evaluate f at each pont by choosing a positive r and a θ in the interval [0 , 2 π )) f ( r, θ ) = θ f ( r, θ ) = r f ( r, θ ) = rθ f ( r, θ ) = r sin( θ ) f ( r, θ ) = r tan( θ ) 8. The kinetic energy of an object is one half the mass times the square of the speed. If an accelerating object gains mass but keeps the same kinetic energy, then what is the rate of change of mass with respect to speed?then what is the rate of change of mass with respect to speed?...
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 Fall '07
 Temkin
 Multivariable Calculus, Cartesian Coordinate System, Energy, René Descartes, lab worker

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