Data from a projectile motion experiment is shown below. Calculate the mean and
ID: 1773370 • Letter: D
Question
Data from a projectile motion experiment is shown below. Calculate the mean and standard deviation for each range. Use the equation for the standard deviation that contains N(N-1). Show one sample calculation in the space below the tables. (Calculation 5 pts, each blank in table 1 pt) Range 1 (m 10.0 12.9 19.7 15.0 Range 2 (m 9.83 13.4 20.2 15.3 Range 3 (m 10.3 12.2 19.5 14.5 Angle Mean ± 20° 40° 60° Use the data above to calculate the mean launch speed of the projectile plus uncertainty by calculating the launch speed for each launch. Assume the launch is on a level surface. Record the mean and uncertainty in the lower right box of the table. Show one sample calculation of the launch speed in the space below the tables. (Calculation 5 pts, each blank in table 1 pt) Launch Speed | | Launch Speed 2 | Launch Speed 3 | Mean ± Angle 15° 40°Explanation / Answer
For angle 150, Mean range=(10.0+9.83+10.3)/3=10.04.
The standard deviation for this angle=((10.0-10.04)2+(9.83-10.04)2+(10.3-10.04)2)1/2/3=(0.0016+0.0441+0.07)1/2/3=0.34/3=0.11.
Similarly following the same procedure to calculate the means and standard deviations for the other 3 angles we
obtain,
For angle 200, Mean m=12.83.
Standard deviation =0.28.
For angle 400 , Mean m=19.8.
Standard deviation=0.17.
For angle 600, Mean m=14.93
Standard deviation=0.19.
To find the launch speed of the projectile for any given range we have to use the formula
Range R=v2sin(2x)/g where x is the angle of projection and v is the launch speed.
For angle 150, v1=(R1*g)/sin2x1)1/2=(10*9.8/sin 300)1/2=1961/2=14 m/s.
Similarly the other 2 launch speeds for the same angle 150 are v2=13.9 m/s and v3=14.2 m/s.
To find the mean speeds and the standard deviation for the given data at this given angle , we use the same procedure as in table 1.
Thus we obtain for angle 150, Mean speed v=14.03 m/s.
Standard deviation =0.07.
For angle 200, the 3 launch speeds for the given ranges are v1=19.3 m/s,v2=19.6 m/s and v3=18.8m/s
The mean and standard deviation for these 3 values are 19.2 m/s and 0.2 m/s.
Similarly for the angle 400, v1=17.4m/s,v2=17.6 m/s and v3=17.3 m/s.
The mean and standard deviation for these 3 values are 17.4 m/s and 0.06 m/s.
Finally for the angle 600, the 3 launch speeds are v1=13 m/s , v2=13.1 m/s and v3=12.8 m/s.
The ,mean and standard deviation of the values for this angle are 12.97 m.s and 0.06 m/s.
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