(III) Early test flights for the space shuttle used a “glider”...

Question

(III) Early test flights for the space shuttle used a “glider” (mass of 980 kg including pilot). After a horizontal launch at 480 km/h at a height of 3200 m, the glider eventually landed at sea level with a speed of 210 km/h.
(a) What would its landing speed have been in the absence of air resistance?

(a) What would its landing speed have been in the absence of air resistance?

Accepted Answer

Welcome back. Everyone in this problem in a competition to advance renewable energy technologies, a solar powered glider with a mass of 850 kg including the pilot is launched from a height of 2000 m above sea level. It attains a forward speed of 350 kilometers per hour under optimal conditions due to air resistance and the design of the glider, it lands with a speed of 150 kilometers per hour. If there had been no air resistance, what would the glider's landing speed have been for our answer choices. A says 783 kilometers per hour. B 794 kilometers per hour c 807 kilometers per hour and d 821 kilometers per hour. Now let's think about what's going on here. So we have a glider, ok. That's launched from a height of 2000 m above sea level. Ok. So let's label that height as edge. Now, we know that our glider, I think probably a glider probably looks something like this, right? And we know that our glider has a mass of 850 kg and it is launched with a forward speed of 350 kilometers per hour. So the initial speed V one, ok, we can label V one oops, we can label the one here as 350 kilometers per hour. And now since we're working, let's first convert that to SI units. So we can multiply it by 1000 m divided by 3600 seconds for the over and in meters per second, it the the speed is gonna be 97.22. Now we know that due to air resistance and the design of the glider, the glider, sorry, it lands with a speed of 150 kilometers per hour. But now we're trying to figure out what its speed would be if there is no air resistance. In other words, when it lands, how fast would it be going? So let me put that in blue here. OK? To represent our glider speed at the bottom of the cliff or the bottom of the height wherever it was launched from. Ok. And now essentially we're trying to figure out the two, that's what we don't know. Well, if we're going to figure out V two, the glider's landing speed, ignoring air resistance, assuming that the only forces acting are gravitational and no air resistance. Then in the absence of air resistance, the total mechanical energy that is the kinetic and potential energy that it had remains constant. So if we use the conservation of energy principle initially, OK. The glider would have potential energy and kinetic energy. OK. But upon landing, ok. Upon landing, then let me share that in blue. You know what? Yeah, let me share that in red. Actually, upon landing, it would only have kinetic energy. OK. And that kinetic energy is what we want to use to figure out what speed it would be going. That is V two. Now here, if we think about it, we know so far that potential energy is equal to the mass of an object multiplied by G the acceleration due to gravity multiplied by the vertical height. And we also know that the kinetic energy is equal to half of the mass of the object multiplied by its velocity squared. So in this case, based on our diagram, and based on our problem, we know that our initial potential energy pe I and our initial kinetic energy ke I is going to be equal to our final kinetic energy kef substituting our formula into that. Then that means mg the mass of the glider multiplied by G multiplied by the height above sea level plus half of MV one squared. The initial kinetic energy is going to be equal to half of MV squared. That is sorry V two squared, that is our final speed squared. OK. Now remember we're solving for V two, we're essentially solving for V two. OK. So that means then that V two squared if we multiply both sets by two and divide by M, then V two squared is going to be equal to two, multiplied by MGH plus half MV one squared. OK. All divided by M. Now, guess what here that means in this problem, uh We're going to be able to divide through by M. OK. So when we divide MGH by M, it's going to be GH and when we divide half MV one squared by M, it's going to be a half of V one squared. OK. So essentially we, we've eliminated M from our formula. Now we have V two squared. So to find V two, we can find the square root of both sides. So that final speed V two then is going to actually be equal to the square root of two multiplied by all of that two multiplied by GH plus half V one squared. Now we can substitute our values because we know what all of those values are. So really, then we're finding the square root of two multiplied by G. Let's take that to be 9.8 m per second squared multiplied by the height uh which is 2000 m plus half of V one squared. So that's half of 97.22 m per second squared. So now to figure out the two, we can put this expression into our calculator. Now, when we do that, OK, we should get the two OK? To be equal to plus or minus 220.57 m per second. We're talking about speed here, physically speed cannot be negative. So we select a positive solution that is V equals 220.57 m per second. Finally, like the rest of our answers, we need to convert this to uh kilometers per hour. OK? And to do that, that means we can multiply it by the reciprocal of our conversion factor as multiplied by 3600 divided by 1000. And then when we do that, we should get it to be equal to 794.1 kilometers per hour, which is approximately equal to 794 kilometers per hour to three significant units. Thus, if there was no air resistance, the speed on landing would have been 794 kilometers per hour. Which when we look back at our answer choices is answer choice. B thanks a lot for watching everyone. I hope this video helped.

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