Midterm Exam 1, Problem 1 – EMA 202, Fall 2013Alternate solutions(1)(d) To find the speed at point C. One could also proceed by using the time it takes Dom to get to point C,(tC)D= d/(v0cos θD) = 0.346 s, and insert this time into the velocity equations:(vCx)D= (v0x)D= v0cos θD= 43.3 ft/s(vCy)D= (v0y)D− g(tC)D= v0sin θD− g(tC)D= 13.85 ft/sThen,(vC)D=q(vCx)2D+ (vCy)2D= 45.5 ft/sMany parts can be solved with aid of a calculator(1) Once it is known that tD= (0.1)tL, to find the time tLwhere the two paths intersect, we rewrite the equations ofmotion for the y-directions:yL= v0sin θLtL−12gt2LandyD= v0sin θD(0.1)tL−12g(0.1)2t2LPlotting both equations on a calculator would shown an intersection:The coordinates of the intersection are at (tL, y) = (2.956 s, 5.98 ft). Thus, the time of intersection happens at tL=2.956 s, which is close to the calculated result reported prior of tL= 2.97 s. Thus, from a previous expression we canwrite the answer for part (b) as ∆t = (0.9)tL= (0.9)(2.956 s) = 2.66 s , which is again basically the same result we gotfrom direct calculations of ∆t = 2.67 s. For part (c), we carry on and note the y-coordinate of collision per the plot isy ' 5.98 ft . Putting in tL= 2.956 s, we find x = v0cos θLtL' 12.9 ft .1Midterm Exam 1, Problem 1 – EMA 202, Fall 2013A final method is more blind: we randomly choose values of tLand compute its corresponding xLand yLfrom thekinematics for Letty, our selection of each tLindicates a corresponding time for Dom’s trajectory: tD= (0.1)tLand wecalculate xDand yDfrom Dom’s kinematic equations. The idea here is to guess such a time that both xL= xDandyL= yD. A presentation of this solution would probably most clearly take the form of a table of values on an exam,where you have a column for each guess for tLthen a list of distances in x and y for D and L. This solution strategy canbe long-going without writing a computer program. Since this is not a numerical methods (programming) course, thismethod is not encouraged in our scope! Notwithstanding, you would not suffer any deduction for successfully carryingout this routine on the
View Full Document
Unlocking...