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Math Help - Calculus kinematics

  1. #1
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    penang
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    Calculus kinematics

    Calculus kinematics please help?

    The height of a baseball hit straight up from the ground with an initial velocity of 64ft/s is given by h=f(t)=64t-16t^2, where t is measured in seconds after the hit.
    a. Is this function one-to-one on the interval 0≤t≤4?
    b. Find the inverse function that gives the time t at which the ball is at height h as the ball travels upward. Express your answer in the form t=f^-1(h)
    c. Find the inverse function that gives the time t at which the ball is at height h as the ball travels downward. Express your answer in the form t=f^-1(h).
    d. At what time is the ball is at a height of 30 ft on the way up?
    e. At what time is the ball is at a height of 10 ft on the way down?

    I really dont know how to do the question for b,c,d and e.

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  2. #2
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    Re: Calculus kinematics

    Fara here are some answers..however you didn't show us any work...
    do not expect us to do your home work...you have to do it by yourself and we will help you.

    Anyway... answers
    a) no it is not ....why? does your function passes the horizontal line test? if yes it is but here.....check it...

    b+c) the inverse function can be found only if you get t<=2 or t> =2 which is the line of symmetry of the parabola h=64t-16t^2
    for t<=2 then the inverse is t=2-sqr[(64-h)/16} while for t>=2 the inverse is t=2+sqr[(64-h)/16}
    How to find this? revise the quadratic function and check how you complete the square and transform your function into completed square form...if you are an I/G student you have studied this in Gr-11. if you have no idea what i am talking about please visit this page :Completing the square - Wikipedia, the free encyclopedia
    d+e) get the appropriate inverse functions and substitute the value of h to get what you need.

    Good luck
    Minoas
    Thanks from fara
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  3. #3
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    penang
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    Re: Calculus kinematics

    I already did the a part actually, but thanks.
    For the b and c part, i really have no idea how to solve the problem, and turns out i just have to complete the square, thanks to you. But i dont really get why the sign of sqrt are different. I assume it is because of the direction that the ball travels, is it? does this related to gravity? since the ball travel upwards so it went to the opposite direction of the gravity force, so that's why the sign is negative before the sqrt?
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