A question about free fall, velocity, and the height of an object. The Next CEO of Stack...
Could a dragon use its wings to swim?
Getting Stale Gas Out of a Gas Tank w/out Dropping the Tank
Decide between Polyglossia and Babel for LuaLaTeX in 2019
"Eavesdropping" vs "Listen in on"
Yu-Gi-Oh cards in Python 3
Why doesn't UK go for the same deal Japan has with EU to resolve Brexit?
Reshaping json / reparing json inside shell script (remove trailing comma)
Are the names of these months realistic?
What was Carter Burke's job for "the company" in Aliens?
Is there a way to save my career from absolute disaster?
Traveling with my 5 year old daughter (as the father) without the mother from Germany to Mexico
Why is the US ranked as #45 in Press Freedom ratings, despite its extremely permissive free speech laws?
Computationally populating tables with probability data
What happened in Rome, when the western empire "fell"?
Does Germany produce more waste than the US?
Can someone explain this formula for calculating Manhattan distance?
IC has pull-down resistors on SMBus lines?
What flight has the highest ratio of timezone difference to flight time?
Can this note be analyzed as a non-chord tone?
Is it okay to majorly distort historical facts while writing a fiction story?
Is it professional to write unrelated content in an almost-empty email?
Reference request: Grassmannian and Plucker coordinates in type B, C, D
Which one is the true statement?
Does destroying a Lich's phylactery destroy the soul within it?
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
asked 3 hours ago
JinzuJinzu
403513
$endgroup$
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
asked 3 hours ago
JinzuJinzu
403513
$endgroup$
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
asked 3 hours ago
JinzuJinzu
403513
$endgroup$
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 3 hours ago
JinzuJinzu
403513
asked 3 hours ago
JinzuJinzu
403513
asked 3 hours ago
JinzuJinzu
403513
asked 3 hours ago
JinzuJinzu
403513
asked 3 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.
answered 3 hours ago
IngixIngix
5,097159
$endgroup$
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 $t=frac{5}{8}$
answered 3 hours ago
E.H.EE.H.E
16.1k11968
$endgroup$
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.
answered 3 hours ago
IngixIngix
5,097159
$endgroup$
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.
answered 3 hours ago
IngixIngix
5,097159
$endgroup$
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.
answered 3 hours ago
IngixIngix
5,097159
$endgroup$
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
answered 3 hours ago
IngixIngix
5,097159
answered 3 hours ago
IngixIngix
5,097159
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 $t=frac{5}{8}$
answered 3 hours ago
E.H.EE.H.E
16.1k11968
$endgroup$
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 $t=frac{5}{8}$
answered 3 hours ago
E.H.EE.H.E
16.1k11968
$endgroup$
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 $t=frac{5}{8}$
answered 3 hours ago
E.H.EE.H.E
16.1k11968
$endgroup$
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
answered 3 hours ago
E.H.EE.H.E
16.1k11968
answered 3 hours ago
E.H.EE.H.E
16.1k11968
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
