Ask Experts Questions for FREE Help !
Ask
    Meagan101's Avatar
    Meagan101 Posts: 1, Reputation: 1
    New Member
     
    #1

    Oct 6, 2009, 04:35 PM
    Polynomial Functions Word Problems (Rates of Change)
    If an arrow is shot upward on the moon with a velocity of 50m/s, its height in metres after t secinds is given by: h(t)= 50(t)-0.83(t)(squared). After how many seconds will the arrow hit the moon's surface? The answer is supposed to be 60.24 seconds but I get every answer BUT that. HELP PLEASE
    elscarta's Avatar
    elscarta Posts: 118, Reputation: 20
    Junior Member
     
    #2

    Oct 6, 2009, 10:22 PM

    When the arrow hits the moon's surface its height = 0 so you need to solve the equation
    0 = 50t - 0.83t^2
    factorising a common factor of t gives
    0 = t(50 - 0.83t)

    this has two solutions

    t= 0 or 50 - 0.83t = 0

    the first solution of t = 0 matches when the arrow was initially fired upwards

    the second solution when 50 - 0.83t = 0 matches when it hits the surface again.

    So you need to solve
    50 - 0.83t = 0
    this means that
    50 = 0.83t
    which leads to
    t = 50 / 0.83

    which gives t = 60.24 s as the answer.

    Hope this helps
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #3

    Oct 6, 2009, 11:20 PM

    If you want to solve this using rate of change, OK.



    Differentiate:





    Solving for t is where the maximum of the equation is maximum, that is the point where the arrow reaches its maximum height.

    Now, solve for t:







    That is the time for half the total journey of the arrow (upwards only). Mutiply by two to get the total time of the journey :)

Not your question? Ask your question View similar questions

 

Question Tools Search this Question
Search this Question:

Advanced Search


Check out some similar questions!

Polynomial word problems [ 1 Answers ]

I need help with this question! I am referencing my text book but I have no idea on where to start with this. I'm not looking for someone to answer the question, just to point me in some kind of direction! If the ticket agency charges ‘p’ dollars per ticket for a concert, it can sell maximum...

Polynomial Functions = Nightmare [ 1 Answers ]

Okay, my pre-calculus teacher isn't very good at explaining things. We're working on graphing polynomial functions, and he went on about them. Unfortunately half the class didn't understand a word he said. So, I would like somebody to guide me through a sample problem (please be very specific,...

Polynomial functions [ 1 Answers ]

consider the function f(x)= x^3+6x^2+9x+4 -state the intervals over which f(x)>0 and f(x)<0 && - show that there is a local maximum at x=3 and state the coordinate.

Polynomial Functions [ 1 Answers ]

Using transformations and the zeros of the polynomial function f(x)=x(x-4)(x+2) how could you determine the zeros of y=f(2x)?? Thanks

Polynomial Functions [ 1 Answers ]

How would you solve x^3-3x^2+2=0? Given P(x)=x^3-2x^2-x+8 how could you use its graph to solve x^3-2x^2>4x-8? Does it show you where it shifts and to what quadrant? I'm confused. What is the solution to x^3-2x^2>4x-8? Thank you.


View more questions Search