A question about free fall, velocity, and the height of an object. The Next CEO of Stack...
Spaces in which all closed sets are regular closed
Is it correct to say moon starry nights?
Expressing the idea of having a very busy time
What connection does MS Office have to Netscape Navigator?
Players Circumventing the limitations of Wish
Physiological effects of huge anime eyes
Can someone explain this formula for calculating Manhattan distance?
Expectation in a stochastic differential equation
Reference request: Grassmannian and Plucker coordinates in type B, C, D
Is it convenient to ask the journal's editor for two additional days to complete a review?
TikZ: How to fill area with a special pattern?
Purpose of level-shifter with same in and out voltages
Is there an equivalent of cd - for cp or mv
If Nick Fury and Coulson already knew about aliens (Kree and Skrull) why did they wait until Thor's appearance to start making weapons?
In the "Harry Potter and the Order of the Phoenix" video game, what potion is used to sabotage Umbridge's speakers?
Lucky Feat: How can "more than one creature spend a luck point to influence the outcome of a roll"?
Can I board the first leg of the flight without having final country's visa?
Decide between Polyglossia and Babel for LuaLaTeX in 2019
Towers in the ocean; How deep can they be built?
How to use ReplaceAll on an expression that contains a rule
Do I need to write [sic] when including a quotation with a number less than 10 that isn't written out?
What was Carter Burke's job for "the company" in Aliens?
What happened in Rome, when the western empire "fell"?
Graph of the history of databases
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
$begingroup$
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):
$$s(t+2) - s(t) = 84$$
$$s(t) = v_0t+cfrac{1}{2}at^2, v_0 = 5, a = 32$$
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
$$64t=10$$
$$t=cfrac{5}{8}$$
$$5left(cfrac{5}{8}right)+16left(cfrac{5}{8}right)^2=9.375$$
$$h_0=109.375$$
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
$$-84=-71t+7t-50$$
$$t=cfrac{34}{71}$$
$$100=-16left(cfrac{34}{71}right)^2+7left(cfrac{34}{71}right)+h_0$$
$$h_0=cfrac{505698}{5041}$$
However the answers are:
$a=cfrac{6475}{65}$
$b=100$
What am I doing wrong?
calculus
$endgroup$
add a comment |
$begingroup$
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):
$$s(t+2) - s(t) = 84$$
$$s(t) = v_0t+cfrac{1}{2}at^2, v_0 = 5, a = 32$$
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
$$64t=10$$
$$t=cfrac{5}{8}$$
$$5left(cfrac{5}{8}right)+16left(cfrac{5}{8}right)^2=9.375$$
$$h_0=109.375$$
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
$$-84=-71t+7t-50$$
$$t=cfrac{34}{71}$$
$$100=-16left(cfrac{34}{71}right)^2+7left(cfrac{34}{71}right)+h_0$$
$$h_0=cfrac{505698}{5041}$$
However the answers are:
$a=cfrac{6475}{65}$
$b=100$
What am I doing wrong?
calculus
$endgroup$
add a comment |
$begingroup$
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):
$$s(t+2) - s(t) = 84$$
$$s(t) = v_0t+cfrac{1}{2}at^2, v_0 = 5, a = 32$$
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
$$64t=10$$
$$t=cfrac{5}{8}$$
$$5left(cfrac{5}{8}right)+16left(cfrac{5}{8}right)^2=9.375$$
$$h_0=109.375$$
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
$$-84=-71t+7t-50$$
$$t=cfrac{34}{71}$$
$$100=-16left(cfrac{34}{71}right)^2+7left(cfrac{34}{71}right)+h_0$$
$$h_0=cfrac{505698}{5041}$$
However the answers are:
$a=cfrac{6475}{65}$
$b=100$
What am I doing wrong?
calculus
$endgroup$
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):
$$s(t+2) - s(t) = 84$$
$$s(t) = v_0t+cfrac{1}{2}at^2, v_0 = 5, a = 32$$
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
$$64t=10$$
$$t=cfrac{5}{8}$$
$$5left(cfrac{5}{8}right)+16left(cfrac{5}{8}right)^2=9.375$$
$$h_0=109.375$$
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
$$-84=-71t+7t-50$$
$$t=cfrac{34}{71}$$
$$100=-16left(cfrac{34}{71}right)^2+7left(cfrac{34}{71}right)+h_0$$
$$h_0=cfrac{505698}{5041}$$
However the answers are:
$a=cfrac{6475}{65}$
$b=100$
What am I doing wrong?
calculus
calculus
asked 4 hours ago
JinzuJinzu
403513
403513
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The error in a) is simple:
From $64t=10$ it follows $t=frac5{32} neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:
$h_0=100+5left(frac58right) + 16left(frac58right)^2=frac{6475}{64}$
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.
$endgroup$
add a comment |
$begingroup$
the solution of
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
should be $t=frac{5}{32}$ not $t=frac{5}{8}$
$endgroup$
add a comment |
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
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
$begingroup$
The error in a) is simple:
From $64t=10$ it follows $t=frac5{32} neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:
$h_0=100+5left(frac58right) + 16left(frac58right)^2=frac{6475}{64}$
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.
$endgroup$
add a comment |
$begingroup$
The error in a) is simple:
From $64t=10$ it follows $t=frac5{32} neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:
$h_0=100+5left(frac58right) + 16left(frac58right)^2=frac{6475}{64}$
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.
$endgroup$
add a comment |
$begingroup$
The error in a) is simple:
From $64t=10$ it follows $t=frac5{32} neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:
$h_0=100+5left(frac58right) + 16left(frac58right)^2=frac{6475}{64}$
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.
$endgroup$
The error in a) is simple:
From $64t=10$ it follows $t=frac5{32} neq frac58$. Substituting this into your formula for $s(t)$ (including that after time $t$ you are at $100$ft) yields:
$h_0=100+5left(frac58right) + 16left(frac58right)^2=frac{6475}{64}$
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.
answered 3 hours ago
IngixIngix
5,097159
5,097159
add a comment |
add a comment |
$begingroup$
the solution of
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
should be $t=frac{5}{32}$ not $t=frac{5}{8}$
$endgroup$
add a comment |
$begingroup$
the solution of
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
should be $t=frac{5}{32}$ not $t=frac{5}{8}$
$endgroup$
add a comment |
$begingroup$
the solution of
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
should be $t=frac{5}{32}$ not $t=frac{5}{8}$
$endgroup$
the solution of
$$left[5(t+2)+16(t+2)^2right]-(5t+16t^2)=84$$
should be $t=frac{5}{32}$ not $t=frac{5}{8}$
answered 3 hours ago
E.H.EE.H.E
16.1k11968
16.1k11968
add a comment |
add a comment |
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.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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