a-hot-air-balloon-has-just-lifted-off-and-is-rising-at-the-constant-rate-of-20-mathrmm-mathrms-sudde

Question

A hot-air balloon has just lifted off and is rising at the constant rate of 2.0 $\mathrm{m} / \mathrm{s} .$ Suddenly one of the passengers realizes she has
left her camera on the ground. A friend picks it up and tosses it
straight upward with an initial speed of 13 $\mathrm{m} / \mathrm{s}$ . If the passenger
is 2.5 $\mathrm{m}$ above her friend when the camera is tossed, how high is
she when the camera reaches her?

Nathan Silvano · Accepted Answer

Okay, so in this problem, we have a hot air balloon rising up. We have constant rates off too, meters per seconds on a person in the balloon and oppression in the ground. Tosses a camera. Two other person in the balloon with constant velocity. Initial velocity. Four of 13 you disburse. Second, the distance between the balloon and the ground was 2.5 meters, and the problem was to discover the final position off the balloon. That&#x27;s mean. That&#x27;s called about whom object A and the camera object to be. So the final position X is going to be the final position off the bottom. So physically, what we know is that when the camera reaches the balloon, the position of the balloon is equal the position of the camera. So we just need to describe the positions of the bathroom and the position off the camera and match both of them. Okay, so what is the position of the bottom about Lou moves with constant rate, which means it&#x27;s going to be X. You&#x27;re away plus VT and right is the positions of the camera. Ex me is just x zero b Poulos visi Vitti. Well, us U GT Square divided by two. We have to notice that the camera is under gravity. The separation which has miners nine point one as value. Okay, so we just need to match X A with X B. So let&#x27;s do this. We&#x27;re going to have X&#x27;s youto, eh? This should be a a waas t because x zero b plus V zero T Poulos U t squared divided by two. Okay, what is the initial positions? Off the bottom? 2.5 velocity. Two initial positions off the camera. Zero because she wasn&#x27;t a ground initial. Velocity. 13 miners, 9.81 divided by two T square. Okay, let&#x27;s rearrange this. We&#x27;re going to have minus nine point 81 t squared, plus 22 two minus five equals zero. This is a contract equation than we know how to solve what attracted equations. Let&#x27;s do another page. We&#x27;re just going to do the solution for the question. Active creation is going to be miners. 22 was minors. Dude square roots. 22 square miners Far times. Mine is 9.81 times minus five. All of these and the Squire roots. Apologies divided by two times minus nine points. 81. Okay, so let&#x27;s see the solution Produce. We&#x27;re going to have to solutions. Fresh solution is going to be time equals your 0.25 I&#x27;ve and the second solution. It&#x27;s going to be 1.99. That point 99 seconds in seconds in here. Okay, So 1.99 this ray bigger. And we have to pick the first time. That is a solution. So we&#x27;re going to solve the equation for a 0.2255 seconds. And the question that we have to solve is this one. We just want to discover the final position off the bottom. So let&#x27;s do this. We have x A equals 2.5 plus two times judo, 0.25 fires. After multiplying all this, we have a final position off 3.2 uh, zero to meters. This is your final answer.

Donald Albin · Answer

All right, we&#x27;ve got a hot air balloon that I&#x27;m just going to draw as a sphere. Mhm. And it&#x27;s descending at a speed of 2.3 m per second. So that&#x27;s going to be velocity. A passenger drops a camera if the camera is 41 m above the ground. So let&#x27;s say the camera is right here and the distance to the ground. Why initial is 41 m? How much time did it take for the camera to reach the ground? Well, why final is why initial plus B. Y. Initial t minus one half G. T squared. Why final needs to be zero because it&#x27;s the ground. Why initial it&#x27;s 41. The initial is negative. Um G is 9.81 half of 9.81 is 4.905 Now we could use the quadratic formula here or we could grab it. I&#x27;m going to go ahead and graph it. So it&#x27;s 41 minus 2.3 t minus 4.905 t squared. And the way Dismas works, if you put in t you gotta put Y equals so that it will actually graph here&#x27;s where it is the ground at one point 44 four seconds and wait a minute. I&#x27;ve only got two significant digits. Okay. And I just found out a mistake that I made and it&#x27;s right here typing it into the calculator. My fingers put in uh 21.3 I think is what they had before. That&#x27;s not right. It&#x27;s supposed to be 2.3. Mhm. And now that does give me 2.66 which is the correct answer. So 2.7 who got around to two significant digits. Okay. Now was the velocity just before it lands? Okay. In part B. By the way, this is part a velocity final is going to be velocity initial minus GT So just putting that into a calculator, velocity initial is negative 2.3 meters per second minus 9.81 m per second times T. Which is the two point seven. Um What do we really have for T. 2.666? I&#x27;m gonna put it that in. So that&#x27;s going to be that upward, be the positive direction. So the velocity is going to be negative 28 and we&#x27;ve only got two significant digits with negative 28 meters per second. Thank you for watching.

Suzanne W. · Answer

At a particular incident, heart Air balloon is 100 m in the air and descending at a constant speed of two m/s. At this exact instant, a girl throws a ball horizontally relative to herself With an initial speed of 20 m/s. When she lands, where will she find the ball? Ignore it? Resistance, So mhm. The hot air balloon is 100 m in the air, so negative 100 m. Is he going to -2 meters per second times t minus one half Gt squared minus 4.9 meters per second squared squared? We know he is equal to 4.3 seconds, solving for tea, We get 4.3 seconds, And so x is 20 m/s Times 4.3 seconds, Which is 86 leaders.

Robert Zaballa · Answer

the balloon is rising up at a constant velocity. So to an observer, uh, moving inside the balloon, the results will not be affected by the fact that they&#x27;re moving up at constant speed. As long as they&#x27;re not accelerating up, they will get the same results as if they were moving or staying on the ground and tossing up the object. So the time to to go up for the object is obtained from the following equation. Velocity for the object that is tossed is a function of time. When it is tossed up is given as V not plus eight times time or plus 80. So the initial velocity of the object that is tossed up is V not equals 12 meters per second. And the acceleration is simply the acceleration due to gravity, which is a equals minus G. And that is negative 9.8 meters per second squared so we can determine how much time it takes for the object to rise up and momentarily stop at its maximum height before it comes back down. And to do that, we will basically set this velocity as a function of time, equal to zero and substitute in the values we know for V not and a So we have 12 meters per second minus g times some value of tea that we&#x27;re trying to determine. And this is then equal to 12 minus 9.8 times the time, and we then have zero equals 12 minus 9.8 times time. We add 9.8 t to both sides and we now have 9.80 equals 12 and weaken divide both sides by 9.8 and we&#x27;ll have the time for the object to rise to its maximum height. So this, then we&#x27;ll cancel. 9.8 will cancel on this side, and this gives us t equals 12/9 0.8, which equals 1.2 seconds. So it takes 1.2 seconds for the object to be tossed up to its maximum height. But this is also going to be the same amount of time it takes for the object to fall from its maximum height. Back down to the balloon, uh, are basically to be caught. So if we double this time, we basically can say that the total time is equal to, and we&#x27;ll just I&#x27;m using Capital T for the total time. So let&#x27;s just label this. Total time is T equals two t, which is 2.4 seconds, and that&#x27;s an equal sign, so there we have it.

Nicholas Majtenyi · Answer

question 74 states that a person holding a lunch bank is moving upward in a hot air balloon and a conference beat of seven meters per second. The balloon is 24 meters above the ground. She accidentally releases the bag. What is this being the bank just before it reaches the ground? So the question of this would benefit from a diagram. So we&#x27;ve got air balloon, never person sitting in the basket or from sure exactly call that this is our balloon Look like a light bulb. I&#x27;m not a drawing on, missy. Um, we&#x27;re at a height. Suppose scene with person drops a bag. This height here called The Distance, is not deep. If this is my bag here, Phyllis box, it gets dropped in falls downward. However, the initial velocity of the bag and the system, the balloon as a whole is giving my feet, not upward. So for this problem, the first thing I&#x27;ll do establish my positive direction, which I call upward to be positive. Okay, so this problem we want to find the final velocity of this bag as it hits the ground. Wait. So in this new, if I just look at what I&#x27;m given. The question I want to use is be not V equals B not be not here is positive This is going upward but my G&#x27;s negative because it&#x27;s going towards around times T I know. Maybe not known. JIA don&#x27;t know t So while this is the one I want to use because I want to solve for V, I need to recognize that I just I need a kingdom an equation to help me find t So we&#x27;re looking the other one distance the height it goes Be not tea. I mean the science minus 1/2 g t square. We&#x27;re going to look at science here. Technically, uhm no, actually, we&#x27;re sure. Fine. Is this yet? No working get sir GT script, right? I just I didn&#x27;t want him to think here. This is actually negative. D is going from a higher height down to a lower height. So this deed should be negative because I&#x27;m falling again towards the negative direction. Great. So I can rearrange this equation and it should look somewhat noticeable. I have, uh, seven t actually playing the value as well. Just like my life is just so it&#x27;s a little more obvious. Perhaps 24 meters deposit here. Of course, because it was negative of the other sign plus 7.0 t minus G over two times. T square is a quadratic point, um, in which you couldn&#x27;t solve. Um, I used it and excel. Use whatever you like. I&#x27;m not gonna show how to solve a Kodak formally here. Just recognize that this is one I shall call Q f. And by doing that, you get to solutions. Um, one being a positive value would be negative. Native in this case doesn&#x27;t make sense. Not physically. A reasonable answer is we take a positive route to be 3.3 seconds. So now if we go over here and the meat that we put that story equation, which I guess looking back again, this should be negative as well, because the velocity as it hits the ground will be going downward so we can find that our velocity is simply are negative. B not minus g t. I can&#x27;t take into account the negative with native um 24 minus 9.8 kinds. 3.3 We solved for this and we find that Our final velocity is negative. 22.7 meters per second. There you go. Um, one slight mistake. While the answer I gave was correct. Um, I actually put it in my distance value, not initial velocity. So they should be excusing seven. Our initial velocity given to us said, we know, minus 9.8 times 3.3, which I guess it was around this to do see them digits to the native 23 meters per second.

Margaret Shawver · Answer

Okay. This problem is where ah, pilot and a hot air balloon suddenly discovers that he is too low to surpass a mountain. It tells us that he&#x27;s speeding toward this mountain at 2.5 meters per second that the mountain is 120 meters away and that he must clear on altitude of 24 meters in order to miss the mountain. The first question is how much time is he had to make this miraculous recovery our normal speed, distance and time equation. Looks like this s equals D over t therefore, to solve for tea, I want to rearrange if s equals d over tea. Then it&#x27;s also true that tea equals d over s and I have all these variables known to me. Distance is 120 meters. Speed is 2.5 meters per second. So t equals 48 seconds. To make this recovery of a lifetime in part B, you want to know what his acceleration needs to be in order to successfully recover? We&#x27;re gonna use this kid a Matic equation. Where d people&#x27;s velocity initial Who us? 1/2 acceleration Times, times, Time square. We know that the velocity is zero. Why is it not 2.5? Because this is the velocity in the UAE direction only. And the problem reads that he was going at a level 2.5 meters a second, so there was no velocity up or down in the wind direction. Therefore, this equation simplifies to D equals 1/2 acceleration time squared as before, only to re arrange to get acceleration all by itself. So I can simply divide by D on both sides or I can divide uh, it would actually be easier to divide by time, squared and then multiply by two on both sides. So a equals two do you divided by t squared? And then it is very easy to do this because we know all these things. That&#x27;s two times 24 again the distance in the why direction divided by t squared, which is 48 squared. And this is going to equal. Please hold. Just honestly, this would cancel toe 1/48 which is equal to zero points 0 to 1 meters per second squared

Problem

Astronauts on a distant planet throw a rock strai…

Problem 101 Hard Difficulty

Answer

3.02 $\mathrm{m}$

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