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Math Help - Please Help Urgent!!

  1. #1
    algebraIIgirl
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    Please Help Urgent!!

    This is a problem in my homework thats due tomorrow please hints?

    The Stratosphere Tower in Las Vegas is 921 feet tall and has a "needle" at the top that extends even higher into the air. A thrill ride called the Big Shot catapults riders 160 feet up the needle and then lets them fall back to the launching pad.

    a. The height h (in feet) of a rider on the Big Shot can be modeled by h=-16t+v(t) + 921 where v is the initial velocity (in feet per second). Find v using the fact that the maximum value of h is 921+160+1081 feet.

    PLEASE HELP IF YOU CAN! we have been solving these kinda of problems but not with two variables!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by algebraIIgirl View Post
    This is a problem in my homework thats due tomorrow please hints?

    The Stratosphere Tower in Las Vegas is 921 feet tall and has a "needle" at the top that extends even higher into the air. A thrill ride called the Big Shot catapults riders 160 feet up the needle and then lets them fall back to the launching pad.

    a. The height h (in feet) of a rider on the Big Shot can be modeled by h=-16t+v(t) + 921 where v is the initial velocity (in feet per second). Find v using the fact that the maximum value of h is 921+160+1081 feet.

    PLEASE HELP IF YOU CAN! we have been solving these kinda of problems but not with two variables!
    There is something very screwy about this problem. Do you mean to say that the height function is
    h = -16t^2 + vt + 921

    Then the function for h is a parabola, opening downward. Put the parabola into standard form by completing the square:
    h = -16 \left ( t^2 - \frac{v}{16} \right ) + 921

    h = -16 \left ( t^2 - \frac{v}{16} + \frac{v^2}{32^2} - \frac{v^2}{32^2} \right ) + 921

    h = -16 \left ( t^2 - \frac{v}{16} + \frac{v^2}{32^2} \right ) + 16 \frac{v^2}{32^2} + 921

    h = -16 \left ( t - \frac{v}{32} \right ) ^2 + \frac{v^2}{64} + 921

    The maximum value for h is going to be at the vertex point. The vertex point here is \left ( \frac{v}{32}, \frac{v^2}{64} + 921 \right )

    Thus we know that
    921+160+1081 = \frac{v^2}{64} + 921
    (Another screwy feature: Why is the number on the left hand side of the equation not given simply as 1162?)

    Now solve for v. I got v = \sqrt{15424}.

    -Dan
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by algebraIIgirl View Post
    This is a problem in my homework thats due tomorrow please hints?

    The Stratosphere Tower in Las Vegas is 921 feet tall and has a "needle" at the top that extends even higher into the air. A thrill ride called the Big Shot catapults riders 160 feet up the needle and then lets them fall back to the launching pad.

    a. The height h (in feet) of a rider on the Big Shot can be modeled by h=-16t+v(t) + 921 where v is the initial velocity (in feet per second). Find v using the fact that the maximum value of h is 921+160+1081 feet.

    PLEASE HELP IF YOU CAN! we have been solving these kinda of problems but not with two variables!
    First your equation is almost certainly wrong, and should be:

    h=-16t^2+vt + 921

    The maximum height occurs midway between the roots of -16t^2+vt + 921, find this point then given you know the height at this point solve the resulting equation for v.

    RonL
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