A question about free fall, velocity, and the height of an object.
$begingroup$
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 Mar 31 at 21:07
JinzuJinzu
410513
$endgroup$
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 Mar 31 at 21:07
JinzuJinzu
410513
$endgroup$
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 Mar 31 at 21:07
JinzuJinzu
410513
$endgroup$
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 Mar 31 at 21:07
JinzuJinzu
410513
asked Mar 31 at 21:07
JinzuJinzu
410513
asked Mar 31 at 21:07
JinzuJinzu
410513
asked Mar 31 at 21:07
JinzuJinzu
410513
asked Mar 31 at 21:07
JinzuJinzu
410513
410513
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 Mar 31 at 21:47
IngixIngix
5,087159
$endgroup$
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 Mar 31 at 21:44
E.H.EE.H.E
16.1k11969
$endgroup$
add a comment |
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
});
}
});
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 Mar 31 at 21:47
IngixIngix
5,087159
$endgroup$
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 Mar 31 at 21:47
IngixIngix
5,087159
$endgroup$
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 Mar 31 at 21:47
IngixIngix
5,087159
$endgroup$
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 Mar 31 at 21:47
IngixIngix
5,087159
answered Mar 31 at 21:47
IngixIngix
5,087159
answered Mar 31 at 21:47
IngixIngix
5,087159
answered Mar 31 at 21:47
IngixIngix
5,087159
5,087159
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 Mar 31 at 21:44
E.H.EE.H.E
16.1k11969
$endgroup$
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 Mar 31 at 21:44
E.H.EE.H.E
16.1k11969
$endgroup$
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 Mar 31 at 21:44
E.H.EE.H.E
16.1k11969
$endgroup$
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 Mar 31 at 21:44
E.H.EE.H.E
16.1k11969
answered Mar 31 at 21:44
E.H.EE.H.E
16.1k11969
answered Mar 31 at 21:44
E.H.EE.H.E
16.1k11969
answered Mar 31 at 21:44
E.H.EE.H.E
16.1k11969
16.1k11969
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
