Unformatted text preview: Chapt. 4 Two and ThreeDimensional Kinematics 41 Now let’s make the nottoolikely assumption that the river velocity in the xdirection is a linear function of y , the distance in the ydirection. Let v x ( y ) = v x max y y max , where y = 0 at the starting shore and v x max = 1 . 5 m / s. How far downstream (i.e., in the x direction) do you move? a) 20 m. b) 40 m. c) 60 m. d) 80 m. e) 100 m. FullAnswer Problems 004 qfull 00200 2 3 0 moderate math: quadratic parabolic 1. The formula for a general quadratic is f ( x ) = ax 2 + bx + c . The shape of a quadratic is actually a simple parabola with the vertical symmetry axis offset from the origin. We will show this in this problem. a) Differentiate f ( x ) and find the stationary point x st by setting df/dx = 0. b) Differentiate df/dx and give the conditions for the stationary point being a maximum and being a minimum. c) By a transformation of the xcoordinate from x to x ′ one can change the equation of the quadratic to that of a simple parabola: i.e.,quadratic to that of a simple parabola: i....
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 Fall '06
 Buchler
 Physics, Trigonometry, Optimization, Trajectory, Quadratic equation, Expression

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