Concept explainers
DATA You have constructed a hair-spray-powered potato gun and want to find the muzzle speed υ0 of the potatoes, the speed they have as they leave the end of the gun barrel. You use the same amount of hair spray each time you fire the gun. And you have confirmed by repeated firings at the same height that the muzzle speed is approximately the same for each firing. You climb on a microwave relay tower (with permission, of course) to launch the potatoes horizontally from different heights above the ground. Your friend measures the height of the gun barrel above the ground and the range R of each potato. You obtain the following data:
Each of the values of h and R has some measurement error: The muzzle speed is not precisely the same each time, and the barrel isn’t precisely horizontal. So you use all of the measurements to get the best estimate of υ0. NO wind is blowing, so you decide to ignore air resistance. You use g = 9.80 m/s2 in your analysis. (a) Select a way to represent the data well as a straight line, (b) Use the slope of the best-fit line from part (a) to calculate the average value of υ0. (c) What would be the horizontal range of a potato that is fired from ground level at an angle of 30.0° above the horizontal? Use the value of υ0 that you calculated in part (b).
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