Exercise A.

a) In the example of the falling object (pp. 72-75), we determined that the height of the ball as a function of time is given by H(t) = H(0) 16t2. If we suppose that the initial height is 100 feet, we get H(t) = 100 16t2. Find the derivative of this function and use it to compute the velocity of the ball at t = 2 seconds.

b) Now estimate how far the ball will drop in the next 0.01 seconds using a linear approximation. In other words, let t = 0.01 seconds, and calculate an approximate value for H.

c) Use the equation of H(t) to calculate the actual change in height from t = 2 s to t = 2.01 s. How different is it from the H you computed at the previous point?