when the lines of code print 'rsquare of linear fit ='rsquared(meanheightsaltitudesand print 'rsquare of quadratic fit ='rsquared(meanheightsaltitudesare inserted after the appropriate calls to pylab plot in processtrajectoriesthey print rsquared of linear fit rsquared of quadratic fit roughly speakingthis tells us that less than of the variation in the measured data can be explained by the linear modelbut more than of the variation can be explained by the quadratic model using computational model now that we have what seems to be good model of our datawe can use this model to help answer questions about our original data one interesting question is the horizontal speed at which the projectile is traveling when it hits the target we might use the following train of thought to design computation that answers this question we know that the trajectory of the projectile is given by formula of the form ax bx ci it is parabola since every parabola is symmetrical around its vertexwe know that its peak occurs halfway between the launch point and the targetcall this value xmid the peak height!"#$is therefore given by !"#$!"#!"# if we ignore air resistance (remember that no model is perfect)we can compute the amount of time it takes for the projectile to fall from ypeak to the height of the targetbecause that is purely function of gravity it is given by the equation ( !"#$%)/ this is also the amount of time it takes for the projectile to travel the horizontal distance from xmid to the targetbecause once it reaches the target it stops moving given the time to go from xmid to the targetwe can easily compute the average horizontal speed of the projectile over that interval if we assume that the projectile was neither accelerating nor decelerating in the horizontal direction during that intervalwe can use the average horizontal speed as an estimate of the horizontal speed when the projectile hits the target figure implements this technique for estimating the horizontal velocity of the projectile this equation can be derived from first principlesbut it is easier to just look it up we found it at the vertical component of the velocity is also easily estimatedsince it is merely the product of the and in figure