VI 1 D cm h cm 1 3 1 3 0 7 0 9 0 4 4 2 3 6 5 8 3 9 4 7 5 9 7 7 8 4 11 2 9 6 16 8 14 7 19 2 19 9 15 4 29 4 23 3 21 1 23 4 22 5 30 6 29 9 32 5 30 6 29 9 38 35 6 40 5 35 6 41 8 50 2 57 5 53 9 49 8 52 2 h D 0 052 0 052 0 028 0 036 0 016 0 14 0 12 0 22 0 24 0 32 0 42 0 3675 0 48 0 4975 0 385 0 52 0 5 0 612 0 598 0 65 0 612 0 598 0 19333333 0 13 0 15666667 0 16857143 0 27428571 0 65333333 0 51777778 0 46888889 0 69090909 0 64727273 0 73636364 0 64727273 0 76 0 83666667 0 95833333 0 89833333 0 83 0 87 25 25 25 25 25 30 30 30 30 30 35 35 35 35 35 40 40 40 40 40 45 45 45 45 45 50 50 50 50 50 55 55 55 55 55 60 60 60 60 60 h D vs D f x 0 02 x 0 6 VI 2 m c D h 1 2 1 0 8 0 6 0 4 0 2 0 20 0 2 25 30 35 40 45 50 55 60 65 D cm VI 3 Using the LINEST function in Excel I calculated the slope s intercept b and the uncertainty for both quantities Slope s Slope uncertainty s 0 02448088 0 00076553 0 6006873 0 03369643 y intercept b Intercept uncertainty b Using the y intercept the experimental launch angle e was calculated by using the following formula b and the uncertainty was calculated using the formula e b 1 b2 For the calculations we have the following We use b and rearrange it so we have tan 1 b e tan 1 b e tan 1 0 6006873 e I then calculated m by averaging all of the angles that were measured with the protractor on the launch track during the experiment After this I calculated the uncertainty in the measured angle m by taking half of the minimum and maximum values measured with the protractor 30 99 31 e e b 1 b2 e 0 03369643 1 0 6006873 2 e 0 02 m 1 2 3 3 m 45 34 40 3 m 39 7 max min m m 45 34 2 2 m 5 5 e e m m 31 0 02 39 7 5 5 Although these values are similar they have different uncertainties Even though these uncertainties are different I feel that e is more reliable than m This is because I used the y intercept that LINEST calculated in Excel This value is more precise because unlike m we measured using the naked eye which can produce a greater amount of uncertainty as seen above VI 4 Using the LINEST calculated slope g 980cm s2 and both of my calculated values of I was able to calculate the launch speed 0 We can refer to the table in VI 3 if slope be calculated using the formula 0 2 slope cos2 g 2 cos2 then the experimental velocity 0 2 0 g exp can Using e 0 Using m 0 exp calc g g 2 slope cos2 2 0 02448088 cos2 31 980 cm s2 165 05 cm s 2 slope cos2 2 0 02448088 cos2 39 7 980 cm s2 183 88 cm s After using my LINEST calculated slope g 980 cm s2 and both of my calculated values of to calculate the launch speed 0 I used the formula M4 13 in the lab manual to help find the uncertainty of the initial velocity My work is as follows for this procedure exp 2 b b 1 b2 2 s 2s 0e 0 6006873 0 03369643 1 0 6006873 2 2 0 00076553 2 0 02448088 2 8 75 cm s 2 b b 1 b2 2 s 2s 0m 0 6006873 0 03369643 1 0 6006873 2 2 0 00076553 2 0 02448088 2 9 75 cm s Using e 0e 0 Using m exp calc 0m 0 165 05 cm s 183 88 cm s exp 0e 0 165 8 75 cm s USING e calc 0m 0 184 9 75 cm s USING m VI 5 I calculated the value of 0 using the formula 0 10 gS 9 So we have the following for the calculation I calculated S 37 5 cm So we have 0 10 gS 9 0 10 980cm s2 37 5 9 0 202 07 cm s2 VI 6 The calculated initial velocity does not agree with the experimental velocity There are many reasons for this to have occurred One reason is that the value of S may have not been measured accurately and the slope may have been off due to inaccuracies in measurements Throughout this experiment there were plenty of room for human error to occur Between the two velocities I believe that the calculated initial velocity will be much closer to the actual result given that the experimental velocities depend on many different measurements As we know the more we measure there are higher chances of error to occur