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Math Help - [SOLVED] SAT math page 657 #18

  1. #1
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    [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?

    Thanks in advance!!

    The correct answer is 70 but why?
    Last edited by fabxx; September 28th 2008 at 03:30 AM.
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  2. #2
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    Hi fabxx,

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

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

    c-d^2=6~~~(*)

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

    All that remains is to solve these two equations simultaneously finding c and d then subbing in t=1 and the values for c and d. Can you continue?
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  3. #3
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    I got d=10 and c=106 and substitute t=1 I got 70 as the final answer!

    Thanks Sean12345!
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