(Chapter Opener Revisited) In the discussion that introduced this chapter, we looked at the graph of the height function of a ball tossed straight up into the air. The following table gives the data from which the graph was constructed; t represents time in seconds after the ball is thrown and H is the height of the ball in feet:
a. Find the quadratic function that best fits these data, rounding all values to four decimal places.
b. Recall that we use the formula h(t) = –16t2 + v0t + h0 to give a projectile’s height h in feet above the ground after t seconds if the projectile’s initial velocity is v0 feet per second and we ignore the effect of air resistance. How does the coefficient of the square term in your model compare to the coefficient in the formula h(t)? Why are they different?
c. If the coefficient of the linear term in your model represents the ball's initial velocity, at what rate was the ball thrown upward?
d. Does the constant term in your model make sense in this situation? Why or why not?
e. If the ball had not been caught at an approximate height of 2.8 feet, at what time would it have hit the ground?
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