1. Pick any football trajectory equation from http://www.carroll.edu/library/thesisArchive/SwensonR_2013.pdf and sample it. Plot the samples. Look at Figure 13. The ball was launched at 120 feet per second. How often must samples be taken so that no measurement of off (during the time interval it represents) by more than one foot?

2. Consider a basketball being dribbled. If the height of the basketball can be described by a sine wave of maximum height 2h, average height h and minimum height 0, and the ball hits the ground once per second, how fast would a video camera have to sample the dribbling to extract its frequency? What happens to the frequency estimate if the sampling rate is too low?

3. If we sample a pure sine signal at "sam" samples per second, and there are 8 samples per cycle of the signal, and we have not undersampled the signal, what is the signal's frequency in cycles per second?

4. Choose any two of the football equations of motion from part 1, and plot them in Octave or Matlab, with colors and line types that distinguish them. Include a legend, and label the plot axes.

Answer 1^st

Initial velocity (u)= (120-20)ft/s = 100ft/s

Distance =D= 1ft

Acceleration = g = 32ft/s^2

We need to calculate the time?

D=ut-1/2*gt^2

Setting the value

We get

1=100*t-0.5*32*t^2

Or 16t^2 -100t+1 = 0

This gives , time= 4.122 second

Now we will calculate frequency

Frequency = 1/time = 1/4.122 = 0.2426 Hz

So, the required number of sample= 0.2426*120 = 29.11 or 29 times.