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Unformatted text preview: CSci 5302 HW5 Due: 22 Apr 2010 Do this homework in pairs, or do part of the homework individually. Even if you do the homework individually, you should understand how to do the remaining problems. 1. ( For everyone) This is another variation on the water hose problem. Suppose the nozzle of a water hose is located at the origin in the ( x, y ) plane, where x is the horizontal direction and y is the vertical direction. The nozzle is shooting water with an initial water velocity v at an angle with respect to the ground ( x direction). The trajectory of the water stream, ignoring air resistance, follows the parabola y =- x 2 g 2( v cos ) 2 + x tan , (1) where g = 9 . 8065m / sec 2 is the acceleration of gravity. One would like to adjust the angle so that the water stream hits a target lying on the roof of a building. The target is located at height y target , but the horizontal distance is variable. We would like to be able to hit this target from as far away as possible, but instead of modelling it by putting the target at a fixed position and moving the source, we model it by fixing the source at (0 , 0) and varying the horizontal coordinate x target of the target. Let the initial water velocity be v = 15m / sec, and the height of the target be fixed at y target = 4m....
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- Spring '08