Assume the units of t are hours. a. Use Matlab to determine the equation for velocity of the weather balloon, using the fact that the velocity is the derivative of the altitude. b. Use Matlab to determine the equation for the acceleration of the weather baloon, using the fact that the acceleration is the derivative of the velocity. c. Use Matlab to determine when the balloon hits the ground. Because h(t) is a fourth-order polynomial, there will be four answers. However, only one answer will be physically meaningful. d. Use Matlab's symbolic plotting capability to create plots of altitude, velocity and acceleration from time zero until the balloon hits the ground. You'll need three separate plots, since altitude, velocity and acceleration all have different units. 2 e. Determine the maximum height reached by the balloon. Use the fact that the velocity of the balloon is zero at the maximum height.