SAT Math Problem. HELP!

Test Preparation
1

<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 b the function h above, in which c and d are positive constants. If the ball reached its maximum height of 106 feet at time
t=2.5, what was the height, in feet of the ball at time t=1?</p>

<p>Lol. Can someone help me? It's the only problem I got wrong on the math section of the practice SAT test. I'm really stumped. Btw it's a bubble in answer, not multi-choice.</p>

2

<p>I’ll move x-axis up by 6’(y = y - 6). Thus at t=0 height (y) = 0 …(1)</p>

<p>The max. height is at t = 2.5 and that would be y = 100…(2)</p>

<p>Then, due to symmetry of flight, y = 0 at t = 5…(3)</p>

<p>We know that flight-time relationship is quadratic …(4)</p>

<ul>
<li>so [using (1), (3) & (5)]</li>
</ul>

<p>y = A * t (5 - t)…(5)</p>

<p>using (2)</p>

<p>A = 16</p>

<p>Thus</p>

<p>y = 16 * t (5 - t)</p>

<p>y(1) = 64</p>

<p>y = y + 6 = 70</p>

<p>ahhh!!! im taking my first sat this jan!</p>

3

<p>LOL! You’re so smart. You answered the question and I didn’t even post the function they were talking about!</p>

<p>h(t)=c-(d-4t)^2</p>

<p>Can you explain where my methodology is flawed?
y=c-(d-4t)^2
y=c+(-d+4t)^2
y=c+16t^2+d^2-8td</p>

<p>For t=0
6=c+16(0)^2+d^2-8(0)d
6=c+d^2</p>

<p>For t=2.5
106=c+16(2.5)^2+d^2-8(2.5)d
106=c+100+d^2-20d
6+20d=c+d^2
Then substitution so…
6+20d=6
d=0</p>

<p>Using substitution…
6=c</p>

<p>But for t=1…
y=6+16(1)^2
y=6+16
y=22</p>

<p>Why am I getting 22 when the answer is 70? Which part of my equations are mathematically unsound? I have tried doing this question over and over, and keep getting the same answer. I must be making a stupid error.</p>

4

<p>

</p>

<p>These are your first 2 steps:</p>

<p>y=c-(d-4t)^2
y=c+(-d+4t)^2</p>

<p>On the surface, they look OK; nothing wrong with factoring out a negative. However, since the (d-4t) is being squared, you can’t factor out the negative sign. You can only do that when the power is 1. You should expand first (i.e. multiply (d-4t)^2) and then do whatever you want to manipulate.</p>

5

<p>lol 3.14159265, love math?
WOOT CLASS OF 2012!!</p>