Activity 2

Last two weeks, we did an experiment on projectile motion to test if the shape of the trajectory of an object undergoing projectile motion is really parabolic as predicted by it's equation. In order to do that we devised our own experiment using projectile guns and ramp. A projectile gun basically looks like this:

We set the angle at which we will fire our gun and let our metal ball hit the wall, leaving a mark on to it. Making the distance from the wall be our independent variable and the height at which the ball hit the wall be dependent variable, we can see that at some points the value of the height is lower and sometimes higher. It may look random when you can see the measurements but when we did the scatter plots of our values, and get it's curve fit, we saw that the path is really parabolic.
Here are the results that we got for 3 angles(15, 30, 45 degrees)

angle: 30 deg
initial y: 20.7 cm
x (cm)	y (cm)	uncertainty
50	39.6	0.1
60	41.75	0.25
70	44	0.6
80	45.45	0.15
90	45.95	0.55
100	44.8	0.4
110	42.55	1.65

angle: 15 deg
initial y: 20 cm
x (cm)	y (cm)	uncertainty
50	22.7	0.2
60	21.95	0.25
70	21.15	0.25
80	20.3	0.5
90	18.35	1.25
100	16.45	0.15
110	14.55	0.95

angle: 45 deg
initial y: 51 cm
x (cm)	y (cm)	uncertainty
50	88.55	0.05
60	94.9	0.1
70	99.85	0.05
80	101.8	0.3
90	104.8	1.2
100	107.5	0.6
110	106.25	0.4

For the angle of 30 degrees, we can see that it's y value increases as we increase the distance from the wall  up to 90. But at 100 cm, the values decreases. This means the maximum height the projectile reached is between 90 and 100. For the 15 and 45 degrees angle, the maximum height value is below 50 cm distance. Since we have the function of the curves generated from this values, we can get the exact maximum point by using some techniques from calculus.