Derive Equations (5) and (6) in the lab write-up. Calculate at what angles the time and range are maximized.

i sari-t ﬁle Edit View History augments wmdaw Help % L: 1 was-u g meet-.117 2:35am. q 5-153 I I 0 t g H itearn.ucr.eeu C ‘ ~.’_ =V 1-—y Yo 03- 281′ Where I0 is the starting horizontal position, yo is the starting height, 1 is the ﬁnal horizontal position, y is the ﬁnalheight, I is the total time-of—ﬂight, and g is the acceleration of gravity. As the ﬁnal height equals the initial height (y= yo) and equation (4) can be easily solved for I:2‘90), t—3 Using equation (2) to substitute for v0, yields: Time-of-ﬂight vs. launching angle 5for one-level projectile motion. ( ) Substituting equations (5) and (1) into equation (3) yields: 2 2 .Range = x _ x0 = 2V0 sine case = Lain 23 Range vs. launching’angle . (6)g g for one-level PIOJﬁClJIE motion. The initial velocity will be determined ﬁ’om your data. You will have two values for initial velocity, one from thetime-of—ﬂight data and one from the range data. Experimental Procedure E erilnent 1: One-level ro’ectﬂe motion. In this experiment you will launch a projectile at different angles andmeasure ﬂre time-of—ﬂight and range (distance traveled) for each angle. Referring to Figure 1, the time will bemeasured by the photogate and the landing pad, which start and stop the timer, respectively. The landing position will be measured by carbon paper (to make a mark) and a ruler. At least three trials will be taken at each angle todetermine the statistical uncertainty of the measurements. Data collection:1. Practice: Load the steel ball into the launcher using a pen or penc