Problem 2 (15 points): Suppose that we perform an experiment to calculate the gravitational con- stant g as follows. We

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Problem 2 15 Points Suppose That We Perform An Experiment To Calculate The Gravitational Con Stant G As Follows We 1 (46.92 KiB) Viewed 15 times

Problem 2 (15 points): Suppose that we perform an experiment to calculate the gravitational con- stant g as follows. We drop a ball from a certain height and measure its distance from the original point at certain time instants. The results of the experiment are shown in the following table: Time (seconds) 1.00 2.00 3.00 Distance (meters) 5.00 19.5 44.0 The equation relating the distance s and the time t at which s is measured is given by: 591 1. Find a least squares estimate of g using the experimental results from the table above.(5 points) 2. Suppose that we take an additional measurement at time t = 4.00 and obtain a distance of 78.5. Use the recursive least-squares algorithm to calculate the updated least squares estimate of g. Verify your solution by solving the problem from scratch with the new measurement and checking if you get the same answer. (10 points)