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An airplane in climbing flight h and an altitude h It maintains uniform speed with a flight path angle Y passes directly over radar tracking station A_ Calculate th...

Question

An airplane in climbing flight h and an altitude h It maintains uniform speed with a flight path angle Y passes directly over radar tracking station A_ Calculate the angular velocity 0 and angular acceleration € of the radar antenna as well as the rate / and acceleration r at which the airplane is moving away from the antenna. Use the equations of this chapter (rather than polar coordinates which you wil use to check your work): Attach the inertial frame of reference to the ground and assume X

An airplane in climbing flight h and an altitude h It maintains uniform speed with a flight path angle Y passes directly over radar tracking station A_ Calculate the angular velocity 0 and angular acceleration € of the radar antenna as well as the rate / and acceleration r at which the airplane is moving away from the antenna. Use the equations of this chapter (rather than polar coordinates which you wil use to check your work): Attach the inertial frame of reference to the ground and assume X nonrotating earth: Attach the moving frame to the antenna, with the X axis pointing always from the antenna toward the airplane. Draw an appropriate diagram and label before solving the problem_



Answers

A radar antenna is tracking a satellite orbiting the earth. At a certain time, the radar screen shows the satellite to be $162 \mathrm{km}$ away. The radar antenna is pointing upward at an angle of $62.3^{\circ}$ from the ground. Find the $x$ and $y$ components (in $\mathrm{km}$ ) of the position vector of the satellite, relative to the antenna.

A spacecraft moving into west to east equatorial orbit is observed by a tracking station located on the equator. This base craft has perigee altitude of 150 km and velocity v when directly over the station And apogee altitude of 1500 km, determine an expression for the angular rate at which the antenna dish must be rotated. When the spacecraft is directly overhead compute he the angular velocity of the earth is omega equals 0.7 to 19 temps into the negative fourth ratings per second. Okay, so first we know that to a is equal to our max plus our men, which means that to a is equal to two are plus 150 plus 1500 which means that A is equal to 71 96 km. So now we have that V squared Is equal to two G. R squared one over r minus one over to a. So at para G, we have that V is equal to 81 79 meters per second, So the angular velocity of the dish the minus our omega over H, and it's relative to the Earth dish angular velocity, which is, he equals P a minus omega. Therefore P is equal to 0.0 514 radiance per second.

Okay, so we're given a question that a plane is flying with velocity off you in X direction at height H in the same direction. And all the data's air given in the diagram is shown. Okay, so angle theta angle five is substandard on Dhere. It is followed by an an Tina. So we need to find the angular velocity off this cantina when the plane is moving with velocity, you and we have to use vertical coordinate. So we know velocity in spherical coordinates are dot You need director, are our data dot You need director theater are five dot You need vector five. Okay, so now we'll first convert this or look this diagram in our X y coordinate. So here, X Y coordinates. So we have velocity. You okay? Which is that some distance Be Then. Let's assume this is a vector here. Ah, and we have an angle of theater were given velocity. You okay, so we can calculate the vector or velocity in our direction, so we'll divide or factories This you velocity into components that is in our and perpendicular to our that will become over theater. Right? You theta. So this is nothing. But in this sense, this angle status we write you cost Tita, and this is you sign. Tita. My Felicia. This factor theater is measured in this direction, but velocity is coming in this direction, so in ticketus Negative. Okay, so we have the components right now, but we have the component at this point, So we need the upward velocity and the radial velocity at are in three excesses. Right. So how well do that? Okay, so for this velocity we have already obtained, you cost data, so we have to multiply by. You cost 54 radial velocity. So for this, we have you cost data times five. So that is caused. Five. Since we need radial one now for five, that is in the direction offset. That is given by same angle. We have same value U cost data, but in this direction so well, right. And that is this one, right? So it is you cost data times sign five because we are measuring in particle direction. But again here, FCC, When the plane moves in this direction, this angle keeps on getting smaller, right? And here we are measuring the angle in cream int so again this early will be negative And the last time leftist Theta one. So we have already calculated the angular velocity of theater, which is this part right in the to deplane ex wife. So here the body is trying to move in the opposite direction as the measurement off angle theta. So that can be written us minus you signed t tough. Okay, so we have all the components. So now we can write our velocity s u cost data cause fight. Then here we have minus you scientific data and that you need vector similarly area where you need factor. And here we have minus you. Cost data signed five. And your directories fight gap. So you can write this answer by clubbing these two. Since we have you cost titter so you cost titter and we get caused. Five are kept minus sign five fight cap and minus you sine theta Detective. So that is a velocity. Okay. Thank you

In this question, we have to find out the X. And the Y. Component of the position of satellite. So to find out the hicks, a component of E. I. Use eggs is equal to X night. Yeah, of course theater here X not is equal to 1 62 kilometer and tita is given us 63 points three degree. So eggs, his Edilberto 75 fine three kilometers. And the Y component is given is why is it why not scientific to? So I he is equal to 162 km into sign into 62.3 Degree. So why component? Uh huh. Yes, 1:43 x three kilometer.

And the rotaries turning about constant rate and equals to 3 60 revolutions per minute in the direction. As shown in the diagram and the nosing at a rate tita dot equals to 0.2 radiant per second. While x, Y Z axes are fixed in the aircraft body. So the angular acceleration of rotor A for theta equals to 30 degrees will be alpha equals two minus treat adults, Jacob cross formula back to So no substituting values. We get first of all, we will determine this omega. Omega will be equals two and multiply by pi by 60 brilliant per second. And direction is minus scientist I kept plus gosh, cheetah cake. Okay, so this is omega vector. So substituting values, we get omega vector equals 23 16 player by to buy by 60 million per second and minus sign protocols to 30 degrees. I kept plus cost 30 degree K cab. So from here after solving we get omega vector equals two minus +65 I kept plus six through three K cab. Okay, so now we will determine this angular acceleration alpha vector. So alfa vector will be equal to minus cheetah dot which is 0.20 point two Jacob cross omega vector, which is complete this value so minus 65 I care plus six route three KK. Okay, so from here, after solving we get angular acceleration vector. Alpha vector equals two minus 1.2 under 35 I kept minus 1.2 by k cab, radiant per second, square radiant per second squared. Ok, so this is the answer for the angular acceleration of rotor A when tita is equal to 30 degrees. Okay?


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