Problem 3: Weather balloons are used to gather atmospheric temperature and pressure data as a function of balloon displacement (i.e., the balloon altitude) The relationship between the balloon displacement (in meters) versus time (in hours), is: h(1) =-0.1214 + 1213-380? + 41001 + 220 Use MATLAB to do the following a. Obtain expressions for the balloon velocity and balloon acceleration. b. Obtain the following plots, in separate figure windows (all for time 0 to 48 hours): i Displacement Ge, Altiude), in meters (on y axis) versus time (in hours) ii. Velocity, in meters per second (on y-axis) versus time (in hours) ii Acceleration, in meters per hr (on y-axis) versus time (in hours) Note: For the Velocity data, make sure to do the appropriate units conversion.] c. Find the value of the maximum displacement (altitude) and the corresponding time. Obtain exact values for these programmatically (not from the plot) Note: Make sure to display the maximum displacement value as a decimal, not as fraction.]