Blue Book page 657 number 18 (problem posted)

Test Preparation SAT Preparation
1

<p>Yes, it's the last question on the Grid-in answers.</p>

<p>Here's the problem:</p>

<p>"h(t) = c – (d – 4t)^2</p>

<p>At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h above, in which c and d are positive constants. If the ball reached its maximum height of 106 at time t = 2.5, what was the height, in feet, of the ball at time t = 1?"</p>

<p>I just don't know how to start solving it. The answer's 70 if you're wondering.</p>

2

<p>I believe you use system of equations to solve for c and d, and then plug those in to solve for h.</p>

<p>You have two equations with only two unknowns (one where h = 6 when t = 0, and one where h = 106 when t = 2.5).</p>

3

<p>^^Liist - did you look in the "Consolidated List ..." thread?</p>

4

<p>Given t = 2.5:
106 = c - (d - 4*2.5)^2
106 = c - d^2 + 20d -100
206 = c - d^2 + 20d</p>

<p>Given t = 0:
6 = c - (d)^2</p>

<p>Thus:
206 = 6 + 20d
20d = 200
d = 10
&
6 = c - d^2
c = 106</p>

<p>When t=1:
h = 106 - (10-4)^2
h = 106 - 36
h = 70</p>

<p>yay, it worked. so skatj was completly right. I don't know if that was the most clear & direct way to do it since I was typing it as I went, but hopefully that helped.</p>