an-object-that-is-initially-thrown-vertically-upward-with-a-speed-of-2-meterssecond-from-a-height-of

Name: an object that is initially thrown vertically upward with a speed of 2 meterssecond from a height of
Uploaded: 2020-06-16
Duration: 4 min 3 s
Channel: Numerade
Description: An object that is initially thrown vertically upward with a speed of 2 meters/second from a height of $h$ meters takes 10 seconds to reach the ground. Set up and solve the initial-value problem that governs the motion of the object, and determine $h$

Question

An object that is initially thrown vertically upward with a speed of 2 meters/second from a height of $h$ meters takes 10 seconds to reach the ground. Set up and solve the initial-value problem that governs the motion of the object, and determine $h$

Michael Jacobsen · Accepted Answer

for this current problem, we have an object that&#x27;s released with from an initial height of zero meters. We&#x27;re told also that the initial velocity upon which it&#x27;s released is two meters per second and finally that after 10 seconds, the object will reach the ground. Given all this information, our job is to solve for the differential equation that governs this motion. Let&#x27;s take the first anti derivative of this equation well, right. D Y t t, which is the expression for velocity, is equal to G Times T plus a constant of integration. Let&#x27;s call this de next. Since we do have initial condition for velocity, let&#x27;s use that information immediately to solve for the variable we have. D Y t t at zero by substitution is G time zero plus D At the same time, D Y t t at zero is too. So too is going to be equal to D. And now our equation is de y t t is equal to g Times T plus two. Next, if we take a further anti derivative, we get the expression for why is equal to G over two times T squared plus two Times T plus Let&#x27;s use another variable of integration and call it, See if we call the C. Then we could go back to the initial height expression and use that information to solve for C. We can write that the height at time zero or why it zero by substitution from the equation that we just found will be equal to G over to time zero squared, plus two times zero plus c But the same time we&#x27;re also told that Wyatt zero is equal toe age. So we have lower case h is equal to see. And now our equation can be updated to why equals g divide by two times t squared plus two times T plus h, which is our initial height Notice. Next that this differential equation will be fully solved assumes we obtain a value for that quantity. H We&#x27;d also have not yet used the initial condition that the height at time 10 seconds is zero. So it&#x27;s used that information next. So by substitution, weaken first right that Wyatt 10 will be G over two times 10 squared or 100 plus two times 10 plus h. Then at the left hand side is zero equals 50 g plus 20 plus age. And finally, the initial height can be solved by writing. H is equal to negative 50 times. She plus 20. Let&#x27;s find out the approximation for this quality through a calculator. This will now be equal to negative 50 times G, which is acceleration due to gravity and since were in units of meters per second, that quantity G is equal to negative 9.807 plus 20. This tells us that H is approximately equal to 470.35 meters. Next weaken Safer answer that the equation that governs the height of this object is why equals G divide by two t&#x27;s word plus two times T plus 470.35 This work then solves this differential equation.

James Kiss · Answer

we&#x27;re working off the equation. H was negative 16 t squared plus piece of zero T plus H ₹0 at Ciro&#x27;s initial acid and agents. Here&#x27;s initial height. We know that a ball is thrown upward from a height of five. That&#x27;s the initial height. With an initial velocity of 11 feet per second, that&#x27;s gonna be 11 t. We want to know what the maximum height is that&#x27;s going to be at the of Vertex. So let&#x27;s locate the Vertex here. Gonna jump over and do this with a graph approach thinking of 16 T or we&#x27;ll call it X squared 11 to you or X plus five. And the question is, what is the maximum height? The maximum height occurs in 0.344 seconds, but the height is about 0.689 So, um, 0.3446 point 891 Yeah, Okay, so in point people four seconds, it reaches a height of approximately 6.891 feet high

Sherrie Fenner · Answer

era in question 51 we will be using the function from from question 60 which is F A T equals negative board White nine. He squared close our mission velocity time. Tea glass too. I was recounting question 60 though I am going to take the derivative of that because we want the reach Max of 200. So I&#x27;m taking derivatives. Um, so negative. 4.9 times to gives me negative 9.8 Jeanne plus these of zero and now been substitutes he ruin for my pride and solved. And now, in my position, equation of good. Couldn&#x27;t my cheese place my p So I have Yeah. Oh, over point No. 19 from eight. I swear. These three ground times Gypsy rose, divided by plus two equals two *** or quite nine. The Pepsi roads where over 98 subzero square eight equal venom is attracted to from both sides on 98. And now I have multiple other. Multiply everything by 9.8 square. You get rid of the denominator, have negative or 0.9 visa zeros. Where lies the square with zero eyes? 9.8 Because the dominator only has one night, but need, innit? People&#x27;s 1 98 I&#x27;m 9.8 square. So now I have, like, terms that I can combine that native 4.9 beasts Shapiro&#x27;s where plus 9.8, These zeros Where gives me positive or 0.9. These have zeros Square. And this e equal owns one. Maybe one 19 0 15 White 92. We&#x27;re gonna divide that by 4.9 and that&#x27;s gonna give me 38 8 equals V sub zero&#x27;s where Take this. We&#x27;re route of that and I get 623 meters per second equals my initial no.

Michael Jacobsen · Answer

in this situation, we have an object whose initial height is given to be H meters or, in other words, why it zero is equal to H. The initial velocity is given to be V not Nor the words D Y t t f zero is be not. And we&#x27;re let letting t not to know the time when the object will hit the ground. Or, in other words, why a t not is zero. So given that differential equation that governs the motion of this object is second derivative, a position equals G will solve this differential equation. The first anti derivative is de y DT Expression for a lot for velocity is equal to g times T plus a constant of integration. See, let&#x27;s all for this constant immediately were given an initial velocity d Y d T f zero is equal to be not so. In other words, de y d t at a time zero by substitution is G time zero plus C from the equation we just found If we input V not by substitution onto the left hand side, we get to be not is equal to see. So in the words see itself as an initial velocity and the equation is now de y d t equals G Times t plus V not Let&#x27;s take a further anti derivative two obtained that why is equal to G divide by two times T squared plus V not Times t plus a new constant integration. Let&#x27;s call this one deep. Now we go to the initial height for initial condition, which will allow for us to solve for the constant D Immediately. We&#x27;re told that toe y at zero is equal to age. But first, let&#x27;s substitute in zero. In place of the very bull T we obtain G over to time zero squared plus V not time zero plus deep and that zero the height is equal to H. So why it zero is h by substitution. And now we see that H is equal to d. Finally, then we have that Our equation for the motion of this object is why equals g divide by two times t squared plus V not Times t plus H Now Ray To obtain the final portion of this problem, recall that t not was meant to be the time the object hits the ground in other words. Why Tina zero If we express why a t not by substituting in Tina from t in our solution will obtain that g over to times t not squared. Plus the initial velocity V not Times t not plus h on the right hand side but on the left hand side is also zero sore equation becomes zero is equal to do you divide by two times t not squared plus v not times t not plus age. And our objective in this problem is to determine what the initial velocity V not must be in this situation. So it&#x27;s solved for V not in this problem. Let&#x27;s take us our next step. Subtract H and the G over to t not squared from both sides and we&#x27;ll obtain negative h minus g over to t not squared is equal to V, not times t not next. We can say V not is equal to negative H minus 2/2 times t not squared. Almost applied by one over t. Not if on our next step we factor out a negative two from inside the parentheses and reorder the one over Tina factor. We could say that v not is equal to one over negative two times t not times H plus G over two times t not or rather, to h plus g times. T not with the power of to on the variable t not, and this solves for what the initial velocity must be nor to satisfy these initial conditions.

Zulfiqar Ali · Answer

only questions for each ball s is equal to its not, ah bliss less be not times D less one divided by two um, times X relation times a T square. Well, four ball A. We have 30 less five T minus one divided by two times nine point age T square. And for do you we have 20 times D minus one divided by two multiply by 9.8 times Are T square Well defined, Uh, the time we have, uh ah. Position off is equal to position of B. So we have QWERTY less. Five D um, minus 4.91 de square is equal to 20. Do you minus, um, four point 91 He square and solving for tea. He is equal to two seconds. Uh, no. Let&#x27;s find out S so it&#x27;s visible to 30 less by multiply by two minus one. Divided by two times nine Going to 81 times two square. So s physical to distance equals 20. Find four meter

Linh Vu · Answer

as a first numpty ico ju ju day one a 16 t square And the question as to to find a maximum height on notice that in this function here and it&#x27;s a quadratic function for the hair is negative fr with judges can&#x27;t aircraft They were the problem and that opened down. So this one is punished. Point him would be the maximum looking for And it go inside stood the vortex Yeah, so I&#x27;m going to find a bit about Thanks you Could you buy formula ico Judah minus p over to buy an F minus playing overt You I So it doesnt lead up. Yeah, and yeah, the money&#x27;s been able to any way EKO joke the Manus tempted to of ah minus June Thames minus do with them on the 60 Aniko jet that Did you ever take you and include you one And then that much off one We go Jew 32 times one minus 16 times going square and were able to their 60. So we have the height the maximum height, cultural 60 at the first on the 1st 2nd on now B s about I in b. We need to fight the number of seconds. It That&#x27;s object. You hit the ground. So it means that we need to find ah ah the X and deceptive. So yeah, it means Then we had to send a attitude day minus 16. The square equals Jizo were affected a 16 day outside in 700 Teoh they could use Oh, they&#x27;re funded three quiches. Oh, and that included you there for the number second vintage it hit the ground will be It will be to monitor and included two seconds.

Problem

An object that is released from a height $h$ mete…

Problem 28 Hard Difficulty

An object that is initially thrown vertically upward with a speed of 2 meters/second from a height of $h$ meters takes 10 seconds to reach the ground. Set up and solve the initial-value problem that governs the motion of the object, and determine $h$

Answer

$y=\frac{9}{2} t^{2}+2 t+470.35$

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$y=\frac{9}{2} t^{2}+2 t+470.35$

Differential Equations and Linear Algebra

Grace H.

Anna Marie V.

Caleb E.

Michael J.

Integration Review - Intro

Definite vs Indefinite

Stephen W. Goode, Scott A. AnninDifferential Equations and Linear Algebra

Grace H.

Anna Marie V.

Caleb E.

Michael J.

Stephen W. Goode, Scott A. Annin

Differential Equations and Linear Algebra