SECTION II
Part A TIME: 30 MINUTES
A graphing calculator is required for some of these problems.
- The Boston Red Sox play in Fenway Park, notorious for its Green Monster, a wall 37 feet tall and
315 feet from home plate at the left-field foul line. Suppose a batter hits a ball 2 feet above home
plate, driving the ball down the left-field line at an initial angle of 30° above the horizontal, with
initial velocity of 120 feet per second. (Since Fenway is near sea level, assume that the
acceleration due to gravity is −32.172 ft/sec^2 .)
(a) Write the parametric equations for the location of the ball t seconds after it has been hit.
(b) At what elevation does the ball hit the wall?
(c) How fast is the ball traveling when it hits the wall? - The table shows the depth of water, W, in a river, as measured at 4-hour intervals during a day-
long flood. Assume that W is a differentiable function of time t.
t (hr) 0 4 8 12 16 20 24W(t) (ft) 32 36 38 37 35 33 32(a) Find the approximate value of W ′(16). Indicate units of measure.
(b) Estimate the average depth of the water, in feet, over the time interval 0 ≤ t ≤ 24 hours by using
a trapezoidal approximation with subintervals of length Δt = 4 hours.
(c) Scientists studying the flooding believe they can model the depth of the water with the function
where F(t) represents the depth of the water, in feet, after t hours. Find F ′(16)
and explain the meaning of your answer, with appropriate units, in terms of the river depth.
(d) Use the function F to find the average depth of the water, in feet, over the time interval 0 ≤ t ≤
24 hours.