A question about free fall, velocity, and the height of an object. The Next CEO of Stack OverflowVelocity Question & AccelerationUp and Down Motion (Two objects meeting in time?)Velocity of a Ball When it Hits the GroundHeight and velocity of ball thrown verticallyRelated rates problem, rocket and observerThrowing a baseball on top of a cliffGiven initial conditions, find the maximum height reached by an object thrown upwards and its velocity on returning to the groundCalculus- Conceptual question about velocity.How does the sign of the acceleration depends on the direction of the distance choosen?Confusion on when velocity and acceleration are positive vs negative

Man transported from Alternate World into ours by a Neutrino Detector

Can you teleport closer to a creature you are Frightened of?

Is it okay to majorly distort historical facts while writing a fiction story?

Won the lottery - how do I keep the money?

How do I fit a non linear curve?

Calculate the Mean mean of two numbers

Can someone explain this formula for calculating Manhattan distance?

Can this note be analyzed as a non-chord tone?

Can I board the first leg of the flight without having final country's visa?

Help/tips for a first time writer?

Do scriptures give a method to recognize a truly self-realized person/jivanmukta?

What can the phrase “is embedded in a whale of a bill” mean?

From jafe to El-Guest

A question about free fall, velocity, and the height of an object.

Spaces in which all closed sets are regular closed

Decide between Polyglossia and Babel for LuaLaTeX in 2019

Does Germany produce more waste than the US?

Why is information "lost" when it got into a black hole?

Traduction de « Life is a roller coaster »

Computationally populating tables with probability data

Where do students learn to solve polynomial equations these days?

Reference request: Grassmannian and Plucker coordinates in type B, C, D

Expectation in a stochastic differential equation

What would be the main consequences for a country leaving the WTO?



A question about free fall, velocity, and the height of an object.



The Next CEO of Stack OverflowVelocity Question & AccelerationUp and Down Motion (Two objects meeting in time?)Velocity of a Ball When it Hits the GroundHeight and velocity of ball thrown verticallyRelated rates problem, rocket and observerThrowing a baseball on top of a cliffGiven initial conditions, find the maximum height reached by an object thrown upwards and its velocity on returning to the groundCalculus- Conceptual question about velocity.How does the sign of the acceleration depends on the direction of the distance choosen?Confusion on when velocity and acceleration are positive vs negative










4












$begingroup$


A falling stone is at a certain instant $100$ feet above the ground. Two seconds later it is only $16$ feet above the ground.



a) If it was thrown downward with an initial speed of $5$ ft/sec, from what height was it thrown?



b) If it was thrown upward with an initial speed of $10$ ft/sec, from what height was it thrown?



I got the wrong answers when working on this.



To solve a):



$$s(t+2) - s(t) = 84$$
$$s(t) = v_0t+cfrac12at^2, v_0 = 5, a = 32$$
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
$$64t=10$$
$$t=cfrac58$$
$$5left(cfrac58right)+16left(cfrac58right)^2=9.375$$
$$h_0=109.375$$



To solve b):



$$100=-16t^2+7t+h_0$$
$$16=-16(t+2)^2+7(t+2)+h_0$$
now subtract the smaller constant from the larger
$$-84=-71t+7t-50$$
$$t=cfrac3471$$
$$100=-16left(cfrac3471right)^2+7left(cfrac3471right)+h_0$$
$$h_0=cfrac5056985041$$



However the answers are:
$a=cfrac647565$
$b=100$



What am I doing wrong?






calculus







share|cite|improve this question









$endgroup$
















    4












    $begingroup$


    A falling stone is at a certain instant $100$ feet above the ground. Two seconds later it is only $16$ feet above the ground.



    a) If it was thrown downward with an initial speed of $5$ ft/sec, from what height was it thrown?



    b) If it was thrown upward with an initial speed of $10$ ft/sec, from what height was it thrown?



    I got the wrong answers when working on this.



    To solve a):



    $$s(t+2) - s(t) = 84$$
    $$s(t) = v_0t+cfrac12at^2, v_0 = 5, a = 32$$
    $$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
    $$64t=10$$
    $$t=cfrac58$$
    $$5left(cfrac58right)+16left(cfrac58right)^2=9.375$$
    $$h_0=109.375$$



    To solve b):



    $$100=-16t^2+7t+h_0$$
    $$16=-16(t+2)^2+7(t+2)+h_0$$
    now subtract the smaller constant from the larger
    $$-84=-71t+7t-50$$
    $$t=cfrac3471$$
    $$100=-16left(cfrac3471right)^2+7left(cfrac3471right)+h_0$$
    $$h_0=cfrac5056985041$$



    However the answers are:
    $a=cfrac647565$
    $b=100$



    What am I doing wrong?






    calculus







    share|cite|improve this question









    $endgroup$














      4












      4








      4





      $begingroup$


      A falling stone is at a certain instant $100$ feet above the ground. Two seconds later it is only $16$ feet above the ground.



      a) If it was thrown downward with an initial speed of $5$ ft/sec, from what height was it thrown?



      b) If it was thrown upward with an initial speed of $10$ ft/sec, from what height was it thrown?



      I got the wrong answers when working on this.



      To solve a):



      $$s(t+2) - s(t) = 84$$
      $$s(t) = v_0t+cfrac12at^2, v_0 = 5, a = 32$$
      $$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
      $$64t=10$$
      $$t=cfrac58$$
      $$5left(cfrac58right)+16left(cfrac58right)^2=9.375$$
      $$h_0=109.375$$



      To solve b):



      $$100=-16t^2+7t+h_0$$
      $$16=-16(t+2)^2+7(t+2)+h_0$$
      now subtract the smaller constant from the larger
      $$-84=-71t+7t-50$$
      $$t=cfrac3471$$
      $$100=-16left(cfrac3471right)^2+7left(cfrac3471right)+h_0$$
      $$h_0=cfrac5056985041$$



      However the answers are:
      $a=cfrac647565$
      $b=100$



      What am I doing wrong?






      calculus







      share|cite|improve this question









      $endgroup$




      A falling stone is at a certain instant $100$ feet above the ground. Two seconds later it is only $16$ feet above the ground.



      a) If it was thrown downward with an initial speed of $5$ ft/sec, from what height was it thrown?



      b) If it was thrown upward with an initial speed of $10$ ft/sec, from what height was it thrown?



      I got the wrong answers when working on this.



      To solve a):



      $$s(t+2) - s(t) = 84$$
      $$s(t) = v_0t+cfrac12at^2, v_0 = 5, a = 32$$
      $$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
      $$64t=10$$
      $$t=cfrac58$$
      $$5left(cfrac58right)+16left(cfrac58right)^2=9.375$$
      $$h_0=109.375$$



      To solve b):



      $$100=-16t^2+7t+h_0$$
      $$16=-16(t+2)^2+7(t+2)+h_0$$
      now subtract the smaller constant from the larger
      $$-84=-71t+7t-50$$
      $$t=cfrac3471$$
      $$100=-16left(cfrac3471right)^2+7left(cfrac3471right)+h_0$$
      $$h_0=cfrac5056985041$$



      However the answers are:
      $a=cfrac647565$
      $b=100$



      What am I doing wrong?






      calculus




      calculus






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 4 hours ago









      JinzuJinzu

      403513




      403513




















          2 Answers
          2






          active

          oldest

          votes


















          1












          $begingroup$

          The error in a) is simple:



          From $64t=10$ it follows $t=frac532 neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:



          $h_0=100+5left(frac58right) + 16left(frac58right)^2=frac647564$



          which is very similar to your answer key (I assume you mistyped the denominator).



          In b) you seem to be calculating with $v_0=7ft/s$, but $v_0=10ft/s$ was given.






          share|cite|improve this answer









          $endgroup$




















            1












            $begingroup$

            the solution of
            $$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
            should be $t=frac532$ not $t=frac58$






            share|cite|improve this answer









            $endgroup$













              Your Answer





              StackExchange.ifUsing("editor", function ()
              return StackExchange.using("mathjaxEditing", function ()
              StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
              StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
              );
              );
              , "mathjax-editing");

              StackExchange.ready(function()
              var channelOptions =
              tags: "".split(" "),
              id: "69"
              ;
              initTagRenderer("".split(" "), "".split(" "), channelOptions);

              StackExchange.using("externalEditor", function()
              // Have to fire editor after snippets, if snippets enabled
              if (StackExchange.settings.snippets.snippetsEnabled)
              StackExchange.using("snippets", function()
              createEditor();
              );

              else
              createEditor();

              );

              function createEditor()
              StackExchange.prepareEditor(
              heartbeatType: 'answer',
              autoActivateHeartbeat: false,
              convertImagesToLinks: true,
              noModals: true,
              showLowRepImageUploadWarning: true,
              reputationToPostImages: 10,
              bindNavPrevention: true,
              postfix: "",
              imageUploader:
              brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
              contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
              allowUrls: true
              ,
              noCode: true, onDemand: true,
              discardSelector: ".discard-answer"
              ,immediatelyShowMarkdownHelp:true
              );



              );













              draft saved

              draft discarded


















              StackExchange.ready(
              function ()
              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3169890%2fa-question-about-free-fall-velocity-and-the-height-of-an-object%23new-answer', 'question_page');

              );

              Post as a guest















              Required, but never shown

























              2 Answers
              2






              active

              oldest

              votes








              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              1












              $begingroup$

              The error in a) is simple:



              From $64t=10$ it follows $t=frac532 neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:



              $h_0=100+5left(frac58right) + 16left(frac58right)^2=frac647564$



              which is very similar to your answer key (I assume you mistyped the denominator).



              In b) you seem to be calculating with $v_0=7ft/s$, but $v_0=10ft/s$ was given.






              share|cite|improve this answer









              $endgroup$

















                1












                $begingroup$

                The error in a) is simple:



                From $64t=10$ it follows $t=frac532 neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:



                $h_0=100+5left(frac58right) + 16left(frac58right)^2=frac647564$



                which is very similar to your answer key (I assume you mistyped the denominator).



                In b) you seem to be calculating with $v_0=7ft/s$, but $v_0=10ft/s$ was given.






                share|cite|improve this answer









                $endgroup$















                  1












                  1








                  1





                  $begingroup$

                  The error in a) is simple:



                  From $64t=10$ it follows $t=frac532 neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:



                  $h_0=100+5left(frac58right) + 16left(frac58right)^2=frac647564$



                  which is very similar to your answer key (I assume you mistyped the denominator).



                  In b) you seem to be calculating with $v_0=7ft/s$, but $v_0=10ft/s$ was given.






                  share|cite|improve this answer









                  $endgroup$



                  The error in a) is simple:



                  From $64t=10$ it follows $t=frac532 neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:



                  $h_0=100+5left(frac58right) + 16left(frac58right)^2=frac647564$



                  which is very similar to your answer key (I assume you mistyped the denominator).



                  In b) you seem to be calculating with $v_0=7ft/s$, but $v_0=10ft/s$ was given.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 3 hours ago









                  IngixIngix

                  5,097159




                  5,097159





















                      1












                      $begingroup$

                      the solution of
                      $$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
                      should be $t=frac532$ not $t=frac58$






                      share|cite|improve this answer









                      $endgroup$

















                        1












                        $begingroup$

                        the solution of
                        $$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
                        should be $t=frac532$ not $t=frac58$






                        share|cite|improve this answer









                        $endgroup$















                          1












                          1








                          1





                          $begingroup$

                          the solution of
                          $$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
                          should be $t=frac532$ not $t=frac58$






                          share|cite|improve this answer









                          $endgroup$



                          the solution of
                          $$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
                          should be $t=frac532$ not $t=frac58$







                          share|cite|improve this answer












                          share|cite|improve this answer



                          share|cite|improve this answer










                          answered 3 hours ago









                          E.H.EE.H.E

                          16.1k11968




                          16.1k11968



























                              draft saved

                              draft discarded
















































                              Thanks for contributing an answer to Mathematics Stack Exchange!


                              • Please be sure to answer the question. Provide details and share your research!

                              But avoid …


                              • Asking for help, clarification, or responding to other answers.

                              • Making statements based on opinion; back them up with references or personal experience.

                              Use MathJax to format equations. MathJax reference.


                              To learn more, see our tips on writing great answers.




                              draft saved


                              draft discarded














                              StackExchange.ready(
                              function ()
                              StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3169890%2fa-question-about-free-fall-velocity-and-the-height-of-an-object%23new-answer', 'question_page');

                              );

                              Post as a guest















                              Required, but never shown





















































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown

































                              Required, but never shown














                              Required, but never shown












                              Required, but never shown







                              Required, but never shown







                              -

                              Popular posts from this blog

                              名間水力發電廠 目录 沿革 設施 鄰近設施 註釋 外部連結 导航菜单23°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.7113923°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.71139計畫概要原始内容臺灣第一座BOT 模式開發的水力發電廠－名間水力電廠名間水力發電廠 水利署首件BOT案原始内容《小檔案》名間電廠 首座BOT水力發電廠原始内容名間電廠BOT - 經濟部水利署中區水資源局编编

                              Image
                              東螺溪清水溪加走寮溪阿里山溪東埔蚋溪獅尾堀清水溪清水溝溪水里溪陳有蘭溪郡坑溪十八重溪那馬嘎班溪松柏坑溪卓棍溪瓠瓢坑溪益則坑溪玉崙溪丹大溪郡大溪巒大溪卡社溪栗栖溪萬大溪萬大北溪萬大南溪霧社溪塔羅灣溪馬赫坡溪萬大發電廠大觀發電廠日月潭第一發電所明潭發電廠...
                              Read more

                              Prove that NP is closed under karp reduction?Space(n) not closed under Karp reductions - what about NTime(n)?Class P is closed under rotation?Prove or disprove that $NL$ is closed under polynomial many-one reductions$mathbfNC_2$ is closed under log-space reductionOn Karp reductionwhen can I know if a class (complexity) is closed under reduction (cook/karp)Check if class $PSPACE$ is closed under polyonomially space reductionIs NPSPACE also closed under polynomial-time reduction and under log-space reduction?Prove PSPACE is closed under complement?Prove PSPACE is closed under union?

                              Image
                              Is a conference paper whose proceedings will be published in IEEE Xplore counted as a publication? Prove that NP is closed under karp reduction? Is it important to consider tone, melody, and musical form while writing a song? How is it possible to have an ability score that is less than 3? Can I make popcorn with any corn? Mathematical cryptic clues tikz: show 0 at the axis origin Minkowski space can i play a electric guitar through a bass amp? Why not use SQL instead of GraphQL? How can I prevent hyper evolved versions of regular creatures from wiping out their cousins? How old can references or sources in a thesis be? Do VLANs within a subnet need to have their own subnet for router on a stick? How to add double frame in tcolorbox? How much RAM could one put in a typical 80386 setup? "You are your self first supporter", a more proper way to say it How is the claim "I am in New York only if I am in America" the same as "If I am ...
                              Read more

                              Is my guitar’s action too high? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Strings too stiff on a recently purchased acoustic guitar | Cort AD880CEIs the action of my guitar really high?Μy little finger is too weak to play guitarWith guitar, how long should I give my fingers to strengthen / callous?When playing a fret the guitar sounds mutedPlaying (Barre) chords up the guitar neckI think my guitar strings are wound too tight and I can't play barre chordsF barre chord on an SG guitarHow to find to the right strings of a barre chord by feel?High action on higher fret on my steel acoustic guitar

                              Image
                              Is the Mordenkainen's Sword spell underpowered? Escaping $ in listings environment Short story about astronauts fertilizing soil with their own bodies No invitation for tourist visa but I want to visit Do regular languages belong to Space(1)? Can I take recommendation from someone I met at a conference? How to name indistinguishable henchmen in a screenplay? Found this skink in my tomato plant bucket. Is he trapped? Or could he leave if he wanted? How can I prevent/balance waiting and turtling as a response to cooldown mechanics Can I feed enough spin up electron to a black hole to affect it's angular momentum? Why does BitLocker not use RSA? Is my guitar’s action too high? Does GDPR cover the collection of data by websites that crawl the web and resell user data Trying to enter the Fox's den How to achieve cat-like agility? "Destructive power" carried by a B-52? Should man-made satellites feature an intelligent inverted "cow c...
                              Read more