Solutions Project 1 Sostegni 996088
Implementation and visualization
The values of the coefficients of the interpolating polynomial of degree 1 are:
- −1·c = 4.212504197285544 100
- −3−2.158423049188220 ·c = 101
Interpolation
Fitting
Interpretation of the results
In order to compute an estimate of the value of v, we have to understand at what instant t, belonging to the interval [0, 150] s, the function becomes constant. Firstly, we set up a while loop in which we compare the difference between the velocity at a certain point t to the next one: this difference has to be smaller than a fixed value we choose, for instance −1210. Executing the code, we obtain that this difference is smaller than the fixed value for an instant t = 82 s.
Once we have this point, we can compute the mean value of the function on the interval [82, 150], which we are assuming as an estimate for v.
t150
Z
1·vest = v(t) dt = 5.169375204026099 10 m/s
t −150 82
82
On the other hand, using the mathematical formula we obtain:
r
gm
1·v = = 5.169375204026111 10 m/s
t
cd
Comparing the two results, we can see that the difference lies in the last 3 decimal digits and its value is −13·1.207922650792170 10: we can definitely say that we computed an excellent approximation.
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