1.(a)(b)
(c)
2.(a)
(b)(c)(d)Part A
TIME: 30 MINUTES
2 PROBLEMS
A graphing calculator is required for some of these problems. See instructions.
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 .)
Write the parametric equations for the location of the ball t seconds
after it has been hit.
At what elevation does the ball hit the wall?
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.Find the approximate value of W′(16). Indicate units of measure.
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.
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.
Use the function F to find the average depth of the water, in feet,
over the time interval 0 ≤ t ≤ 24 hours.