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  • Question
  • A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height?


  • Options
  • A. 2.87 sec
  • B. 3.44 sec
  • C. 4.65 sec
  • D. 5.41 sec

  • Correct Answer
  • 3.44 sec 

    Explanation

    It is launched vertically with an initial speed of 110 ft/sec.

    It will reach maximum height when the speed drops to 0.

    Vo=110 feet per second 

    ho=2 feet 

    So, h(t) = -16t^2 +110t +2 

    Take the derivative: h'(t) = 110 -32t 

    The maximum height will be at the inflection when the derivative crosses the x-axis, then h'(t)=0. 

    So, set h'(t)=0 and solve for t: 

    0 = 110 -32t 

    -110 = -32t 

    t=3.4375 

    t=3.44 seconds.

     

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    Comments

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    harry
    I have been searching about this query and got this article here: which is a complete answer in detail and best for all those players who want the detailed answer.


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