Use MATLAB or Octave to solve the problems unless mentioned otherwise. 1. A physical model for free fall is z = gt2, where z = z(t) is the height, t is the time, and g is the gravitational acceleration. The gravitational acceleration can be determined by carrying out the following experiment. A sandbag is dropped from N different heights 2,, i = 1,..., N, and the times t,, i = 1,..., N, required for the sandbag to reach the ground are measured. There is assumed to be an additive random error in the measurement of height. In that case, the observation model can be written in the form of z h(0;t)+v, where is the unknown parameter vector and vis the random error. Write the observation models (pen and paper) for the following cases by treating systematic errors as model parameters when 1 (a) there is a systematic error 20 in the measurement of height, that is Zobs = Zreal 20. (b) there is a systematic error to in the measurement of time, that is tobs = treal + to, and (c) there is additive systematic errors in the measurements of both height and time. Simulate the effects of errors in all above mentioned cases by using MATLAB. Visualize and explain the simulation results. How would you solve the value of g by using the model?