## Sample Interview Questions

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#### 10-27

###### 2021

```Hi, my name is Madeleine and I’ve just finished my second year of Engineering at Jesus College, Cambridge. I applied in 2012 and matriculated in 2013. I’m going to go through 2 interview questions which are taken from the website I want to study Engineering.org which is a website which has hundreds of engineering interview type questions with worked through answers and occasionally videos too. The two questions that I’m going to do are similar to the kind of questions that I got during my interviews. So hopefully this will help.

So the first question reads as follows. On a clear day, you are on an airplane which is 38,000 ft above the middle of Pacific Ocean. Taking the radius of the Earth to be 6,400km, what is the approximate distance between you & the horizon of the Earth? You are also given that 1 foot is equivalent to 0.3048 meters.

So the first thing that I would do is convert the 30000 feet into meters using the given conversion. So 38 000 ft times by 0.3048 meters is roughly, using a calculator, 11.6km So now that you have all of the figures in meters or km, you can then draw a diagram of the earth with the center here and you can say that the airplane is hereish. So now marking the distances on, you know that this, the radius of the earth, is 6400km. I’m just going to say all the distances are in Km. Then the distance from the plane to the Pacific Ocean is, as we calculated here, 11.6kms. So now we need to think about where the horizon is. So the horizon is the line of sight from where you are in the airplane to the first point you can see. By definition or by intuition, you can say that point has to be at right angles with the radius of the earth because if you are looking at this way and say that this is your line of sight and this is always the horizon and it’s essentially where your line is horizontal with the circumference of the earth. So if we then draw the radius of the earth on to this point you know this has to be a right angle and, so from then on, it’s essentially a Pythagoras question. So again this is the radius of the earth and you are trying to find the approximate distance between you and the horizon. So if we call this x (that’s the distance here). So then if we redraw the triangle, we have x here, 6400km here and, in total, 6411.6 here and so by Pythagoras which in full of course is this and by rearranging this to get x; as the result, you find the x, the approximate distance between you and the horizon of the earth is roughly 386km.

The second question which is I’m going to go through goes as follows. A rocket of mass m is to be launched from the surface of a rogue planet with mass M and radius R and no atmosphere. By making reasonable assumptions about the distance between the planet and any nearby galaxies, find the escape velocity required for the rocket to overcome the gravitational field of the planet.

You might be wondering what the reasonable assumptions mentioned in the questions might mean. And you just really need to think about what the effect of other planets close by to this planet might be. So if there are planets close to the rogue planet, it’s likely that their gravitational field that have an effect on the motion of the rocket. Therefore, the assumption that you need to make is the distance between this planet and any nearby planets is very, very large and, therefore, only the gravitational field of the rogue planet is important in this question.

So for this question, I’ll go straight into drawing a diagram as it might make it clearer as to what you need to do to solve this problem. Say this is the planet and we can mark on here that this is the radius big R. Now if we draw the rocket to be here at any moment in time, we can label the distance from the rocket to the center of the earth as little r. So this is just something that we can define. Say in another given time, the rocket has now moved. So it’s got a little further and we are going to say that the distance between this instance and this instance is delta r (just to symbolize a little distance). So we know that as the rocket is moving, there must be a force due to the gravitational field of this planet acting on the rocket and this force is going to be in this direction which we can call big F and we know in this instance it will also be acting obviously with a different value which is given by the formula F equals big G and then the mass of the planet which is capital M, the mass of the body upon which the force is acting which is the little m over the distance between the two bodies which we have to find as r2.

Now with kinetic energy questions, you often immediately think of energy balancing equations. So this might help in this problem. One energy balance equation that we know is that the work done is equal to force times distance. Although we don’t quite know how we are going to get to kinetic energy through this, it might be worth a try. We know that the force on the rocket is going to be given by the equation that we just wrote down and if you don’t remember this equation in the interview or you haven’t seen it before just as an example in an interview if you can’t think of the equation or you really don’t know it; if you just state it, say “I’m really sorry I don’t think I can’t quite really remember the formula of the equation” They will usually give it to you as it will help you solve the question and they just don’t want you to stop in your tracks so they will help you if you forget things that might be useful.

So yes force times this force times the little distance. So we are working out the work that’s done for the rocket moving from here to here. So we will do times delta r. Now this here is just an equation for the little amount of work done moving the rocket from this position to this position which is just an arbitrary small distance. So to get the total amount of work that will be needed to get the rocket from the surface of the earth as specified in the question all the way to outside the gravitational field of the planet we will need to sum all these little works done from bigger to infinity which is where the gravitational field of the planet will end. Now if this isn’t an intuitive step and you don’t get it in the interview, they may again the interviewers may again help you so that you might be able to proceed further with the question. So don’t panic.

Therefore the total work done which I’m going to write as w will be equal to the integral between big R (so the radius of the planet) and infinity of this. And now you can see it’s just an integral but we need to calculate to get the work done. So to do the integral, you can rewrite the over r2 as r to the power of -2 which makes it easier and then you can see that by adding 1, dividing by the new power you get minus … r to -1 which you can put on the bottom again between R to infinity. Now this when you put the limits in, the first limit you put in is infinity obviously dividing by infinity is going to give you zero and then the next step is you are doing is minus and then inserting large R; so you end up with a minus minus big G big M little m over big R. Now this is just the total work done. So I’ve just moved the result of this integral up here to save space for the next bit of the question.

As I have said in the beginning, when you think of kinetic energy questions you may think of work done and energy balance equations. So now we have the total work needed to get the rocket from here to outside the gravitational field. Through energy balance, you know that the work done that is needed to do this must be equal to the initial kinetic energy that the rocket has when it’s at the surface of the planet. Therefore, we can write that the result of our integral must be equal to half mv squared. From now on, it’s just rearranging to find the v which is the escape velocity, as specified in the question. So mv2 is 2GMm over big R; therefore, in the end you get v as equal to 2GbigM/R as the two ms cancel and the whole thing square rooted. And this is the formula for the escape velocity.

So these were the two interview questions. I hope you found them useful. If you want to see anymore, go to the website that I mentioned earlier, I want to study Engineering.org. But if I were to give any tips for the interview, I would say try not to panic I know it’s really hard and obviously you are going to feel stressed. But if you forget anything in a spark of moment, if you misremember an equation or if you literally can’t see where this question is going, don’t be afraid to admit that. The interviewers are there to help and I’m sure teacher or whoever might have been telling you that already.

You may not believe but it is true they will try and help you through a question they won’t just leave you in an alert they just want to test you with things that you haven’t seen before so maybe using equations that you might have seen in Math and Physics for example the gravitational force equation and then use it in a way that you might not be familiar with. So they just want to see how well you pick up new concepts or at least that’s the idea that I got from my interview and speaking to my interviewers who are now also my supervisors. That is generally the thing that they are trying to do or, at least in my college, that’s what they are trying to do. So try and not to panic and don’t be afraid to admit if you don’t know something. I quoted FM = a in my interview and they still let me in. So don’t worry if you slip up. Try and enjoy it these are some of the most intelligent academics in the engineering field who will be interviewing you probably. They really are there to try and test you obviously but they will also help you through it. So they are not the enemy. So hopefully that was useful and I wish you all good luck.```