# Thread: [SOLVED] SAT math page 657 #18

1. ## [SOLVED] SAT math page 657 #18

h(t)=c-(d-4t)^2

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 feet at the time t=2.5, what was the height, in feet, of the ball at time t=1?

The correct answer is 70 but why?

2. Hi fabxx,

We have $\displaystyle h(t)=c-(d-4t)^2$ . Note that in the text it states, "at time $\displaystyle t=0$, a ball was thrown upward from an initial height of $\displaystyle 6$ feet" so we can let $\displaystyle t=0$ and $\displaystyle h=6$ . This yields $\displaystyle h(1)=c-d^2=6$ . Call this equation $\displaystyle (*)$ . Also note in the text; "$\displaystyle 106$ feet at the time $\displaystyle t=2.5$" thus letting $\displaystyle t=\frac{5}{2}$ and $\displaystyle h=106$ we have $\displaystyle h\left(\frac{5}{2}\right)=c-\left[d-4\left(\frac{5}{2}\right)\right]^2=c-(d-10)^2=106$ . Define this as equation $\displaystyle (**)$.

Now we have two equations with two unknowns, namely $\displaystyle c$ and $\displaystyle d$;

$\displaystyle c-d^2=6~~~(*)$

$\displaystyle c-(d-10)^2=106~~~(**)$

All that remains is to solve these two equations simultaneously finding $\displaystyle c$ and $\displaystyle d$ then subbing in $\displaystyle t=1$ and the values for $\displaystyle c$ and $\displaystyle d$. Can you continue?

3. I got d=10 and c=106 and substitute t=1 I got 70 as the final answer!

Thanks Sean12345!