because-a-rocket-blasts-off-and-moves-straight-upward-from-the-launch-pad-with-constant-acceleration

Question

$\because$ A rocket blasts off and moves straight upward from the launch
pad with constant acceleration. After 2.8 s the rocket is at a height
of 91 $\mathrm{m}$ . (a) What are the magnitude and direction of the rocket's
acceleration? (b) What is its speed at this time?

Nathan Silvano · Accepted Answer

So in this problem, we have a rocket moving upwards, Uh, most into still oration. And the problem say&#x27;s that after a time off, 2.8 seconds, he has ah, Hight School X. He has a height off nine. You want meters? Okay, so this is the information we have and the problem wants to know what was the magnitude off the acceleration. So we want to know what was, uh, acceleration. And what is the velocity at this moment? Okay, so and this problem, we&#x27;re going to years to immigrations first aggression. It&#x27;s going to be the position as a function of time zero plus zero t plus a T square divided by two. And the second creation is going to be the velocity as a function of time. Me, Chris is, you know, plus 80 why we&#x27;re doing the speakers. We only have two informations about the problem. We have the position in the time. So if we want to discover the velocity, we need a recreation that has final velocity and has in half time. And we for one to discover acceleration. We have to use equation. They only needs the information. We haven&#x27;t a problem That&#x27;s why we using this equation first. So let&#x27;s go. That&#x27;s a silly question. So the first item we have to discover their celebration, so we&#x27;re going to use the first creation acts. Eco&#x27;s eggs eared of philosphy zero t well US 82 divided by two. So 91 is our height. Exterior is here because of the initial position v 00 because the initial velocity So we have acceleration times two point eight square divided by two. So the acceleration is going to be. It&#x27;s seen its to the calculation. Here it&#x27;s going to be 91 Pull us times two Divided by two point eight square. This is equals two 20 23 points 21 meters per second square. This is the celebration of the rocket and the second item it&#x27;s going to be going to use the second Gration that is the e grows fee zero plus 80. So the final velocity it&#x27;s just the acceleration that is 23 points 21 21 times two point eight seconds. So velocity is just 60 five meters per second. That&#x27;s the final answer. Thanks for watching

Justin Hameline · Answer

problem 31 of Chapter two states. A rocket rises with constant acceleration to an altitude of 85 kilometers, at which point its speed is 2.8 kilometers per second are a then asks us what is the acceleration in order to solve for this what we want to dio its first write down the information that we have given as I&#x27;ve done on this left side, we know that our initial velocity and our initial height are going to be zero because our final velocity and final height were given in the problem by 85 kilometers as our final Hyatt and 2.8 kilometers per second as our final velocity. With this information, we can use the two Kinnah Matic equations I&#x27;ve written down on the right side which are final. Velocity squared is equal to initial velocity squared plus two times the acceleration times Why as well as the other equation, final velocity is equal to initial velocity plus acceleration times time in order to solve for part a. What we want to dio is used the first equation nuts. We have VF squared equals V I squared plus two a. Why this can then be rewritten as VF squared minus the I squared, divided by two. Why is equal to a From here we can just plug in our values that we have written down in the top left intern giving us the value for a to the 0.46 meters per second squared. Be then asks us How long is the scent Take this can then be solved using the second equation I have written down the uh equals V I plus 80. This can be rewritten to be via minus V. I divided by okay is equal to t from here by plugging in the values of as we have found for our our acceleration and our final velocities, we know that the final time on the ascent takes 60.87 seconds, thus giving us this solution.

Nathan Silvano · Answer

Okay, So in this problem we have a rocket moving upwards. If our acceleration off to Ralph meters per second square, the rockets maintain his deceleration until he reaches the height off 29 meters. After this moment after disposition Hey, shut off his changing and continue its flight in free fall. Okay, so the first question is, what is the maximum height? Let&#x27;s go Ex Toto off the after rocket What is the maximum height that the rocket reaches? Okay, so first of all, let&#x27;s think about entire movement. Let&#x27;s see, we have our rocket moving from rest with acceleration of 12 meters per second squared. Then the rockets reaches first position. Ex ICO swan disposition. He shut offs his angel and continues moving upwards. And so he reaches a maximum height school ex too, and stop! The thing that we have to notice is that in this segment off the movement, his acceleration is the gravity&#x27;s acceleration off miners nine point 81. So actually we have two movements. The first movement is ah accelerated movement. And the 2nd 1 is a decelerated movement. So we need to use two equations to calculate it, each off them separately. Okay, so let&#x27;s calculate this. The first part of the movement is the accelerated move movement. So we want to find out the height. So let&#x27;s see, to calculate the maximum height, we need to discover the velocity. So, in the first part of the movements, we have these where it goes easier square. Well, us too. A doubt ex. Sorry. That&#x27;s call X one. So you guys can not get confused. This is going to be ex. What? Okay, so V, we don&#x27;t know. The zero is zero because he starts addressed, plus two times 12. And the first position we know is 29. So actually, the first velocity, the maximum velocity, it&#x27;s going to be 69 six. So the square root 696 It&#x27;s just 26.4 meters per second. So this is the first velocity. This is the velocity. A position X one. When we have the position X one, the final velocity, his 26 point for. Okay, so come back here. Now we have the velocity off the final position. We can just cover there. Position x two. So the position next to we&#x27;re going to use this immigration is just going to be the square equals to visit or square. Well, it&#x27;s true. G Delta Not doubt. That&#x27;s put ah X two in here x two. So let&#x27;s see. Their final velocity is your toe. The initial velocity is the fine of a lost such of the first part. So it&#x27;s just 69 Six miners, two times nine points. 81. It is the gravity&#x27;s acceleration now pointing downwards times the x two. Let&#x27;s get these X here. Okay, so let&#x27;s see the distance x two Just going to be, uh let&#x27;s see. 35 35 point 47 meters. So the answer to the first item, What is the maximum height that we call ext E X Toto? Just going to be x one plus x two. So this is finally 64 point 47 meters. This is the maximum height of the rockets. Okay, Next item the next item we need to calculate what is the speed of the rocket just before reaching the ground. Okay, so this time now we have 1/3 part of the movement. Let&#x27;s come back in here. See? Still rockets stop. Here we begin a turd art of the movement that is, the rockets beginning to fall under the gravity&#x27;s acceleration one to reach the ground. This is a free falling object. So in this part, off the movement, we can use again the same equation which are me to square because the zero less too times g Delta X So v zero is what we want to discover is your RV is what we want to discover Vizier is, you know, because in the beginning of the third part of the movement the beginning of the dirt art off their movement, the rocket starts from rest. So these ears just sooner. Plus two times nine point 81 Delta X Delta access the Toto space. The maximum height. It was just going to be 64 0.47. So calculating this, we have the answer to this second item. The velocity of the rocket just before reaching the ground is going to be dirty. Five point 57 meters per seconds. Okay, so the dirt item the eye can see we want to discover. I did told told oration off the rockets flights. So the total duration of the rockets fight we just need to use what information we have from the previous calculation. So we just need to use the vehicles, visit Europe, Loss 80. So let&#x27;s see. First of all, we need to calculate the time off each off their movements separately because you don&#x27;t have to. We don&#x27;t have a way to calculate it all the time. In one single calculation, we need to separate this movement. So the first part of the movement we start with initial velocity of zero with acceleration of 12. We need to find a time in the final velocity we know, which is. It&#x27;s just 96.4. So this is going to be 26.4. So their first time going to be 26.4 divided by 12. This is a code 2.2 seconds. The second part off their movement. We have another time. Vehicles 30 plus GT. This time we&#x27;re going to have V zero. V zero is 26.4 minors, 9.81 e. So the second time it&#x27;s going to be 26.4, divided by 9.81. This is just 2.7 seconds and the final part of the movement. They&#x27;re free. Falling from his maximum right height is just vehicles Visitor loss GT so V we already calculated this was 35 0.57 s is equal to zero plus 9.81 key. So the final time waas 35 point 57 divided by nine point 81. This is going to be equal to three points 62 seconds. So the answer to the final letter final writing is that total time it&#x27;s going to be to a point too. Plus 2.7 lost 3.62. This is going to be equal to eight point 52 seconds and this is the final answer to the problem. Thanks.

Ryan Hood · Answer

In order to calculate the average velocities, we&#x27;re going to need the velocity at the start in the end of the four point seven five second part. So if we assume that our initial losses zero when the rockets on the ground, we&#x27;re trying to solve for the final velocity after the one point one five seconds. So that will be our unknown. The time will be one point one five seconds and the distance traveled during the initial one point one five seconds is sixty three meters. Now we&#x27;re going to use the Kinnah Matic equation X minus X not is equal to one half be not plus b times t When were we plug in these values we get sixty three is equal to one half in this case be nada zero So that term goes away. So we&#x27;re just left with B times one point one five solving for the yields one hundred and nine point five seven meters per second. So this is the velocity at the beginning of the four point seven five second part. Now any of the velocity at the end of the four point seven five second part and to do this we&#x27;LL treat this velocity as the initial velocity and then calculate the new final velocity. So now Wien on is equal to one hundred nine point five seven meters per second. This is again are unknown. In this case, he is equal to four point seven five seconds and x minus X not is equal to a thousand minus sixty three because that&#x27;s the new distance traveled by the rocket during the four point seven five second. If it ends at a thousand and one sixty three the first time. Then it went the difference during the four point seven five second part. This is called a nine hundred three seven meters, and we&#x27;re going to use the same chromatic equation. X My sex night is equal to one half Levin on plus B comes T Nuria plug in so you get nine hundred thirty seven is equal to one half. Be not is now no longer. Zero. It&#x27;s one hundred nine point five seven plus V times four point seven five. Our unknown has B, and this is just an algebraic equation. At this point, solving it gives is equal to two hundred and eighty four point nine six meters per second and now we can actually start to calculate the things we need. Calculate. So for the four point seven five second part, the average velocity is the final velocity which is two hundred eighty four point nine six, Right, This guy minus the initial velocity which is one hundred nine point five seven when we divide. By the time that that took, which is four point seven five seconds and I get thirty six point nine two meters per second, I&#x27;m going to do the other part on the next page. So for part B, we need the full five point nine seconds, including the beginning of the takeoff and then the four point seven five second part. So for fool, five point nine seconds, the average Flossie is equal to the final velocity which is still two hundred eighty four point nine six. But now the initial velocity zero because originally have to be any of the five point nine six. It was moving at zero velocity and in the time it takes is five point nine seconds and what I get is forty eight point three meters per second, which is the answer to part me

Zachary Warner · Answer

for this question. We&#x27;re considering a rocket taking off on. We&#x27;re told that it travels a distance which I called D one of 63 meters and a time which I call t one of 1.15 seconds. We&#x27;re then told that after 4.75 more seconds so t to the rockets total distance traveled is 1000 meters. So d one plus d to is 1000 meters on Ben. T two is 4.75 seconds. So the total time to travel 1000 meters would be t one plus tea too. For part A were asked to find the average velocity. Um, there has to find the average velocity for the 4.75 2nd part of the flight or other words. In other words, for the tea to part of the flight. Well, the velocity for that part will call this Visa Bay. Since this is the velocity for part, A is going to be equal to the distance traveled for that part, which would be D too, right? So how do we find D too? Well, we just simply take our value of d one plus D two, which was 1000 meters and we subtract the one from that right And that would give us d too, which the one we know is 63 meters and this needs to be divided by the time it takes to travel that distance d to which was T too. So we plug our values into this expression. We find that this is 197 meters per second, which would give me which weaken boxing is our solution. For part a part B wants us to find the average velocity for the entire trip. Well, the average velocity for the entire trip will call this visa be. Since this is the lost he calculated in part, B is going to be equal to the distance traveled for the entire trip the one plus D to which we know is 1000 meters. Um, I didn&#x27;t mention this, but I converted kilometers into meters. We told we&#x27;re told it&#x27;s one kilometer which is equal to 1000 meters, and it&#x27;s gonna be divided by the time it takes to travel that distance which will be t one plus tea too. So if you notice the way the question worded it, it says for the 1st 5.9 seconds of the flight, but T one plus t two is 5.9 seconds. So that&#x27;s where I got t one plus tt from. So he plugged those guys into this expression and the Sequels. 169 meters per second. This could be boxed in is our solution for part B and that is the final part of this question.

Nathan Silvano · Answer

So in this problem we have ah rocket Launch a and the rocket rises into a height off four points to meters. Okay. And this moment he has Ah, the lost city off 26 meters per seconds. Okay, if problem wants to know, how much time does it take to get to his height and with what acceleration? Hey, this is the two things we must answer the first items and the final in the final item, we have to answer. What is the height? Let&#x27;s go x one. And what is the velocity right after 0.1 seconds off the lunch. The launch. Okay, so first of all, we&#x27;re going to use three equations in this problem. I&#x27;m goingto intermarry then so we can simplify the faint. The first creation is going to be the phone. Did velocity in function off time? The second the creation is going to be the velocity in Foshan of space loss, eh? Sorry. They&#x27;re strong. Plus two a displacement. And the third a creation is going to be the space as a function of time. Okay, so let&#x27;s go. Ah, the first thing we&#x27;re going to find out is to it&#x27;s the second item the item be when we have to find the magnitude of acceleration because it&#x27;s easier and to find acceleration. We going to use this second aggression creation too. Let&#x27;s go. So we have fi square Cruz V zero square. Well, us too. A displacement. Okay, Uh, the final velocity is 26 square equals to zero because it is the initial velocity plus two a times the displacement. What is the displacement of displacement? Waas 4.2. So the acceleration off the rocket is just 676 divided by a point for two. Then the acceleration is 80 point for seven meters per second squared. This is the acceleration off their rockets. Okay, so the first item first I tend we want to find out what was the time. So the time we&#x27;re going to use the first equation, The first immigration is let&#x27;s see, going to use the first equation. The first equation, this V was V zero plus 80. Okay, it acceleration. We already have. So the final velocity was 26 initial velocity zero. The acceleration is 18.4 seven t. Okay, So the time that we took to get to this height is just 26 divided by 80 point for seven. This is equals two 0.3 23 sacraments. This is the answer to the first itin. Okay, finally, the final lighting. We have to discover the the height and the velocity. When on Lee, 0.1 seconds has passed since the beginning of the lunch. So let&#x27;s go. Ah, we can use to discover the height the equation three. That is the distance with as a function of time. Okay, so let&#x27;s go we have then X equals x zero. It&#x27;s 00 is also zero day initial velocity. So is just 80 square divided like to this is going to be 80 point for seven times 0.1 square, divided by two. So this is equals two zero going 402 meters. This is the height a 0.1 seconds of the rocket and the final thing we have to calculate it is the final velocity, uh, 0.1 seconds. So let&#x27;s see. For this we go into use the first equation. The first equation is V who&#x27;s zero plus 18. So V is what we want to discover. Zero is also zero acceleration is 80.47 times 0.1. That was the time. So this is Eve course too. The crows too. Uh, see 8.0 for seven meters per second. This is velocity at 0.1 seconds off the launch. Well, that&#x27;s the final answer. Thanks for watching.

Problem

$. .$ Predict/Calculate You are driving through t…

Problem 54 Medium Difficulty

$\because$ A rocket blasts off and moves straight upward from the launch
pad with constant acceleration. After 2.8 s the rocket is at a height
of 91 $\mathrm{m}$ . (a) What are the magnitude and direction of the rocket's
acceleration? (b) What is its speed at this time?

Answer

(a) 23.2 $\mathrm{m} / \mathrm{sec}^{2}$
(b) 65 $\mathrm{m} / \mathrm{sec}$

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James S. Walker

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(a) 23.2 $\mathrm{m} / \mathrm{sec}^{2}$(b) 65 $\mathrm{m} / \mathrm{sec}$

Physics

Christina K.

Liev B.

Farnaz M.

Aspen F.

Math Review - Intro

Algebra - Example 1

James S. WalkerPhysics

Christina K.

Liev B.

Farnaz M.

Aspen F.

(a) 23.2 $\mathrm{m} / \mathrm{sec}^{2}$
(b) 65 $\mathrm{m} / \mathrm{sec}$

James S. Walker

Physics