THEORYThe motion of the projectile may be thought of as the result of two separate,simultaneously occurring components of motion.One component is along a horizontal direction without any acceleration and the other along the vertical direction with constant acceleration due to the force of gravity,this acceleration is directed vertically downward.Thereforeax=0, ay=-g components of initial velocityvix=vicos viy=visinFrom the kinematics equationsXf=xi+vixt+1/2axt2 (1)Yf=yi+viyt+1/2ayt2 (2) (1) Becomes,using ax=0xf-xi=vixttherefore the horizontal range/distance,x= vicos t(2) Becomes,using ay=-g Yf-yi= viyt-1/2gt2y=01/2gt2= viyt1/2gt2= visin tTherefore time of flight t=2 visin/g

To find the initial velocityVi=xi/tiAngleXi (in m)*10-2ti (in sec)Vi (initial velocity)m/svicos

visin

4501100.03193.132.2132.213

2100.02394.182.9552.955

AngleXi (in m)*10-2ti (in sec)Vi (initial velocity)m/svicos

visin

6001100.03253.0771.5392.665

2100.02414.1492.0753.593

To find the horizontal ranget=2 visin/g x= vicos t, % error of range X 100

Anglet measured (s)t Calculated (s)x measured (m)x calculated (m)% error of range

4510.51620.4341.72.96044%

20..66120.60321.7811%

6010.61800.544.8.8374.6%

20.79640.7331.671.5208.9%

To find the average value, standard deviation and SDOMAnglex calculated (m)x (m)x - x(m)( x - x )2

451.9601.37- 0.410.1681

21.780.410.1681

( x - x )2 =0.3362

601.8371.179-0.3420.1169

21.5200.3420.1169

( x - x )2 =0.2338

For = 45Average value x = 1.39 mStandard deviation = 2 = x 0.3362 = 0.1681 = 0.41

SDOM = =.41 / = 0.29

x = (1.37 .29)m

For = 60Average value x = 1.179 mStandard deviation = 2 = x 0.2338 = 0.1169 = 0.34

SDOM = =0.34 / = 0.24

x = (1.179 0.24)m

CONCLUSIONFrom the recorded readings the initial velocity,horizontal range and time of flight are calculated for two different angles.The calculated values for time and range are compared with the measured values,there will be some variations in these values.The % error for the range is also tabulated.For the graphical analysis, gragh is drawn by taking time in the x-axis and horizontal range in the y-axis.