solve-the-given-problems-in-a-modern-hotel-where-the-elevators-are-directly-observable-from-the-lo-2

Question

Solve the given problems.
In a modern hotel, where the elevators are directly observable from the lobby area (and a person can see from the elevators), a person in the lobby observes one of the elevators rising at the rate of $12.0 \mathrm{ft} / \mathrm{s}$. If the person was $50.0 \mathrm{ft}$ from the elevator when it left the lobby, how fast is the angle of elevation of the line of sight to the elevator increasing $10.0 \mathrm{s}$ later?

Daphne Pusey · Accepted Answer

alright in this problem, we have a man that is standing up here on a ledge and he is viewing an elevator going up a clear shaft. All right, So here&#x27;s my elevator car. His standing horizontally from the elevator shaft. 20 meters. He&#x27;s also 20 meters high on this balcony or ledge, and the elevator is rising at a rate of five meters per second. Okay, so horizontal line of sight is going to be here. Okay, so what are we trying to find? We&#x27;re trying to find how quickly the angle of elevation is changing. Okay, so our angle of elevation, if he&#x27;s looking at the elevator, be here. So Fada is going to be this angle. So how quickly is defeated? Et changing and the first instance? We want to know when the height of the elevator is at 10 meters. Okay, so we&#x27;re going to look at the tangent because when the height of the elevator is 10 meters, this distance here is also 10. So we&#x27;re gonna have the tangent of fado is equal to H over 20 or opposite over adjacent. Okay, so we&#x27;re gonna take the derivative of both sides with respect to t So I&#x27;m gonna have seek in squared data de Sade a d t. Is equal to 1/20 a d h d t. All right, so we&#x27;re gonna substitute in now. Sequent squared off. Well, what is data? Okay, so we&#x27;re gonna come down here and say, Well, tangent off, Ada, at this point, exactly this point, it&#x27;s going to be 10/20. Their fourth Aita is going to be negative. 0.4636 radiance. Hey, because we&#x27;re looking down so we can look at this as a negative 10 from our angle of elevation. So seeking squared of negative 0.4636 do you say to DT is what we&#x27;re trying to find is equal to 1/20 and we know D H D T is five. Okay, so this was going to give us 1.25. Di Fada DT is equal to 1/4 and the fate a d. T. Is equal to 0.2 radiance per second. All right, so the next thing we want to know is how quickly our anguish changing when the height is 40 meters. So we&#x27;ll say that&#x27;s up here. Okay, Well, when this is 40 are our opposite Here is going to be 20. Were just looking from here to here is 20 now, this is our fate. Oh, so we can go ahead straight from the derivative we already established here and just go ahead and substitute in so seek and squared off. Now we need to find the angle again. All right, so here, we&#x27;re gonna have Tangent of data is equal to while it&#x27;s gonna be 20/20 and data then is going to be 0.7854 radiance. So 0.7854 times de Seda d team is equal to once again. 1/20 times five. So we&#x27;re gonna have to defeat. Aditi is equal to 1/4 and Di Fada DT this equal to 1/8. Radiant her second

Melissa Salvador · Answer

Okay, so here we want to find the high pub pink building. So here&#x27;s what we&#x27;re gonna do, Gram. First, any one of you is find, um, this right here to the distance between the two buildings because that would give us this right here. All right, so, um, we&#x27;ll see. We&#x27;re going to dio You want to find this angle, so we know that this right here is a right, um, angle. So we&#x27;re gonna do 90 minus 2072. This angle right here. 70. Can we have one side? We want to find the other side. So we have the side of Jason went to find aside opposite. So we&#x27;re going to dio the tangent off 70 is equal to opposite X. So was right here over adjacent, which is study. And so we get that X would be into all right. So if this right here is 82 let me running it in. This is 82. This right here is gonna be 82 as well. And so with that, we can find this site because we have angle inside. So we have another tensions of tangent of 50 is going to be opposite which we don&#x27;t know. We&#x27;re gonna call. Why? Why? Over adjacent, which is the 82. And so we did imagine. Get that. Why would be 98 point here pointed. Okay, so this right here is 98.2. And so then what is this? I This side right here is, um, parallel to the site by there. And so this one is also 30 to the heart of the whole building. All right. Would be 98. It was 30 which is gonna give us 128. And this was all, like approximated to this would be is approximately 128 feet.

Melissa Salvador · Answer

Okay, so here we have a plane that is 10,500 feet above the ground beyond the angle of depression, 30 degrees and 15 minutes. And we want to find, um basically the length of this blue line to this right here. So we know that this side is also going to be, um, 10,500 feet. And so first, let&#x27;s comfort those 13 degrees in 30 minutes into the reason of decimals and you get 30 plus 50/60 which is equal to 13.83 So we have opposite and adjacent, so we&#x27;re gonna use changing ancient off. The 13.83 is equal to opposite, which is 10 1005 100 over adjacent, which we want to find, and then something for X. Forget that that length would be before it. It doesn&#x27;t 641 be

Melissa Salvador · Answer

So in this one, we have a however balloon that&#x27;s going up and want to know how fast it&#x27;s going up. So first someone season at this point point they and then a point beat and we want to figure out how fast it&#x27;s going. So we need to find this side so all of this side, but also when you define this All right, so let&#x27;s find Thanks. So we&#x27;re gonna go with the big one, The big angle. So it&#x27;s gonna be 58 silk. We have opposite and adjacent Sarah Kay Agent Well, 58 as equal to x over 2 50 So, you know, we&#x27;re gonna multiply 250 times attentions of 58 and so that gives us 400. Um, meters, It&#x27;ll do x when we did the same thing with the little triangles and have using attention. 24 is equal to wide over 2 50 we&#x27;re multiplied 250 times detention to 24. We get 111 meters. Do you want to wife now? What we need to find is this distance you&#x27;re here between a and B, so that means that we&#x27;re gonna be subtracted. So we&#x27;re gonna be doing only 400 minus 111. You said then that would equal 280 nine meters. Now, Um, no, we need to find how fast. So speed is equal to distance of 289 over time. And we know that the balloon changed positions in after two minutes. So after two minutes, there was a, um the person&#x27;s all the change in the angle of immolation until within a divided by two. So then this wouldn&#x27;t give us 144 oh, meters a minute. We want our answer and looters for seconds and that we&#x27;re going to divide by 60. Some 20 minute has 60 seconds. Also there only just divide by 60. So then the heart everyone is going up at a rate of 2.41 meters. We&#x27;re sick. So this right here would be our answers

Melissa Salvador · Answer

certain this problem. We have a tree and they want to find the heightened three. We&#x27;re gonna label that so we know that the angle of elevation from the hikers, um, point of view is 75 degrees and he is standing 80 feet away from the tree. And so we have the opposite time. The adjacent side toe. Once again, we&#x27;re gonna use change int. So Ancient of 75 a sequel to the height of the three X about it by 80 feet. So we multiply by 80. So we&#x27;re gonna put this in a calculator and to the nearest foot on the height of the tree would be 299 feet inducts our answer.

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Solve the given problems. A crate of weight $w$ i…

Problem 28 Easy Difficulty

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus