????(????) = ????0 + ????0???????? ????(????) = ????0 + ????0???????? 1 2 ???????? 2 ????0???? = ????0 cos(????0 ) ; ????0???? = ????0 sin(????0) ???????????????????? = ????0???? ???? ???????????????????? = (???????????????????????? ????0) = ????0 2 ????????????(2????0) ???? where ????0 = ???????????????????? ???????????????????????????????? = 2???????????????????????? ???? ???????????????????????? = ???????????????????????? ???????? ???????????????????? = 50 ????; ???? = ???????????????????????????????????????? ???????????????? = 0.13 ???????? ; ????0 = ???????????????????? ???????????????????? (???????? ????????????????????????????) ???????????????? = ???????????????????????????? ???????????????? ???????????????????????????? ???????????????????????? ???????????????????? ???????????????????? = ???????????????? ???????? ???????????????? ???????????????? ???????????????? ???????????????????? ????(????) = ???? (????????????????????????????????????)???????????????????????????????????? ???????? ???????? ???????????????????????????????????????? ???????? ???????????????? ???? ????(????) = ???? (????????????????????????????????)???????????????????????????????????? ???????? ???????? ???????????????????????????????????? ???????? ???????????????? ???? ???? = 9.8 ???? ???? 2 Your submission for this competency test must include the following (all contained within a single .doc or .pdf document): 1. For launch angles of 30o , 45o , and 60o , calculate and plot using Excel the flight trajectories (y(t) vs. x(t)). Hint: you'll want to first use the trajectory equations provided to calculate x(t) and y(t) at t values ranging from 0, 0.01, 0.02, 0.03, ... up to the point at which the y(t) coordinate returns to zero. Then create a xy-scatter plot with x(t) giving the x-coordinates for the plot and y(t) giving the ycoordinates for the plot. Copy and paste the trajectory plots into a word document. Be sure the axes on your plots are labeled, and the title shows which launch angle was used to generate them. 2. For each launch angle (30o , 45o , and 60o ), use the provided formulas to calculate tymax, Range, and time of flight for the projectile (time to reach xfinal). Report your findings in a table. Copy and paste the table of final values into your .doc or .pdf file for submission. 3. Assume that the only information you have is launch distance and launch angle. How can you use the equations provided in this assignment to calculate the quantity of kinetic energy that got transferred to the projective (i.e., t-ball) at launch? [Hint: you will need one equation to calculate V0 and one equation to calculate the kinetic energy at launch]. Describe how you could use these two equations to determine your device's efficiency (hint: for 100% efficiency in performance, the stored energy of 50 Joules should be equal to the kinetic energy at launch). You do not need to actually do any calculations for this question - you just need to be able to show and describe which equations you would use to ultimately estimate your device's efficiency.