solve-the-given-problems-in-testing-a-heat-seeking-rocket-it-is-always-moving-directly-toward-a-re-2

Question

Solve the given problems.
In testing a heat-seeking rocket, it is always moving directly toward a remote-controlled aircraft. At a certain instant, the distance $r(	ext { in } \mathrm{km})$ from the rocket to the aircraft is $r=\frac{100}{1-\cos 	heta},$ where
$	heta$ is the angle between their directions of flight. Find $d r / d 	heta$ for $	heta=120^{\circ} .$ See Fig. 27.4

Maninder Singh · Accepted Answer

let it is the height of the rocket, which is fired straight up. And this is the position off the Observer, which is one mile away from here, one mile away. Let us complete this drinking. No. If t ties the angle, Yeah, we have to find the value off edge in terms. Off feet, not in mice, but in Phoebe&#x27;s. We know that one mile one mine equals five to it&#x27;s zero feet 5 to 80 feet. So therefore, using this relation from this drinker, we have danger teeth, huh? Equals or was it what I just said at or one might that work one month? But we know one might is five to a zero feet sort. Engine Tita equals work 5 to 80 feet, 52 years, zero feet. And from here, we get that he goes 52 What? You can write fire to a zero being June. I do it. Zero danger, Which is the required fight in terms off feet? No. If we have different values of theta, we can find the height, for example. That has take equals this exclusivity. That s dictator equal 60 degree. So that becomes five to it zero into danger and 60. And we know that the engine 60 is scary tree. So therefore, edge equals by to fight to a zero scare three feet. So like this way for different values Off teeter, you can find different heights off the rocket.

Darshan Maheshwari · Answer

talk about a problem. 16 9 Sylvie were given trying like figure, which is actually denials to our transmitting to radar stations Diva and Tito. And here we have a rocket city presented by our the angle of elevations of the Proofpoint secular. This is 28.1 degrees on from here. Bitsangou The time Well, it&#x27;s given us 79.5 all right, the distance between people and reduce. Also given us 1.3 kilometer on we&#x27;re supposed to find does distance which is distance off the of those surveyed Artist station rocket birth pocket with blacking station one treating people. So this is the medics. First of all, let&#x27;s find this angle So this angle will be if this&#x27;ll angle If I Let&#x27;s name it Anger Tito So I&#x27;m gonna take you Will be 1 80 miners because I&#x27;m gonna compete. Straight line is quality, so it could be one in t minus 79 Foreign fire on this will be hung riddle point flights. So this is the value off anger people. Now let&#x27;s use lof fight legs first. I know the value of Angola, so I Millar will be won t minus even plus Tito which is 1 18 minus 28.1 plus 100 point Faith. So this one coming one point four degrees which is you&#x27;ll find a lot. Okay, lets go Use lof science now So we have people do over sign our is equal to X We have to find over fine plug in the values here So dont do is given 1.7 c uh, eyes 7 51 Buying full X is something which we have to find and detours under 0.500 flights. Let&#x27;s do a cross multiplication. Yes. So we have excess 1.73 I am signing off on Rick 0.5. We&#x27;re sign off to find food. When we sold us, we get the value of backsides You point what it the unit will be You know this is the distance off their distance from the radio transmitter

Jake Steedman · Answer

share, you&#x27;ll be taken back to your married white board, where you can begin reporting when you&#x27;re ready to stop.

Mitchel Vereen · Answer

So here we have ah rocket whose acceleration components are given by acceleration. In the extractions equal, the Al Fatih squared an acceleration in the UAE directions equal debate a minus gamma, T and alphabet and gamma are given. So we need to do is we need to find the velocity vector and the position vector as functions of time. So we&#x27;re going to do that by just taking the integral of the acceleration vector so glossy in the X direction as a function of time, we&#x27;re gonna take the integral and that&#x27;s gonna give one third Alfa t cubed and then we have toe add a constant. So the constant we have to add is the initial velocity in the X direction and B y take the in store of you again and we get beta t minus one half gamma t squared. And again we have to add the constant, uh, initial velocity in the Y direction. So to find the velocity vector, we just put those two together. When we get one third Alfa, he cubed plus me, not an extraction. And that is in the I had directions and plus beta t minus one half gamma he squared plus B not why in the J Hat direction. So now to find a position vector Oh, yes. All we have to do is take the derivative of that of the velocity vector. So position vector, we&#x27;re gonna X is function t It&#x27;s gonna be equal to one 12th Alfa T to the fourth plus the not X Times key waas our constant again which we&#x27;re gonna call X nut and for why we&#x27;re going to get one half beta t squared minus 16 gamma t cute and then we have to add a a constant. Now it says that the rockets starts at the origin so we know that X not, And why not? Are going to be zero. So putting together and get the position vector are it&#x27;s gonna be equal to when 12th alfa t to the fourth plus veena x t the I had direction plus one half beta t squared minus 16 Cama He cute in the J hat direction? No, we have to do next is fined the maximum height and so the maximum height is going to be given If we look at a trajectory here, the maximum height is going to be where de velocity in the Y direction. So v y will be equal to zero. So we&#x27;ll do yes, that will take this equation right here. View why and said it equal to zero. So zero equal to beta, which is nine times t minus one half 1.4 zero he squared and then plus V not in the Y direction we&#x27;re given is seven no. And so, using quadratic formula, we see t is equal to 13.6 seconds. You also get a negative number. But since time here can only be positive, we&#x27;re going to use a positive value. And now, since we&#x27;re using, we want to find the height. We plug it into this formula right here because now we know time. So why is equal to seven times 13.6 plus when half times nine times 13.6 squared, minus 1/6 times, 1.4 times 13 0.6 and that&#x27;ll be cute. So, figuring all that out we get, why ends up being 340.6 m Now See, it just wants us to sketch the path we have our X and R y and we start at the origin. It just creates a narc. And now we want to find the distance, the horizontal distance when the rocket returns back to the ground. So we want to find what&#x27;s this is X. We want to find this distance right there. So how we&#x27;re going to do that? The time to get to the top of the ark is 13.6, which means the time to get all the way back down to the ground is going to be double that. So 27.2, then all we have to do is plug that time in into the formula we have for X. So X is going to equal one times 27.2 plus 1/12 times 2.5 times 27.2 to the fourth and then doing all that we find, the X is going to be 114,000 m

Mayukh Banik · Answer

So what happens over here is you were shooting the rocket up this inclined plane at a mangled absolutely the logical so immediately you can, you know, if they&#x27;re not, is the initial without city. You can find the horizon&#x27;s of competent of article company the velocity Andi The rocket travels 100 meter on the inside surface because you know that the self so theoretically with the implying with the horizontal you can find the hard vertical and the horizontal competent, which is the horizontal bubble. If here is X and the radical carpet is negative 15 because it is going downward now. Ah, the horizontal motion is ah, uniformed motion. No acceleration. So you can write the horizontal coming in the last three months, but by time and the rider displacement ease given by this expression where you have the initial that&#x27;s people spread by time minus the half Judy spread because the acceleration use down the Lord Direction G. Now from here extracts sign as for and extract or sign houses from this tree question and they quit the ones with that, it will get an expression off. Ah, aquatic expression on time on every other. Very this known. So, Saul, 40 square from the aquatic equation. You get the quadratic value of peaceful, which is to 50.5 and 1.6 42nd. Do a squirt of that. He did the questioning times. Now, 10. As for the alfa angle over here, you find that, uh, corresponding to the 15.89 you get 4.17 billion corresponding to 1.27 seconds. You&#x27;d better value 115 which does not agree to our situation. So the only angle that we have is 4.17 dig me. And now, in the vertical direction, we find the maximum hide. In order to find the massive height, we want to know when the massive heart offers the Time T is found by the expression B Y equals zero. So from the y equals zero, we find the time that getting over here and then find that the article height The maximum height is 284 major

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Solve the given problems. The number $N$ of refle…

Problem 57 Easy Difficulty

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Precalculus Review - Intro

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

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