On September 8, 2004, the Genesis spacecraft crashed in the Utah ...

Question

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The 210-kg capsule hit the ground at 311 km/h and penetrated the soil to a depth of 81.0 cm. (a) What was its acceleration (in m/s2 and in g’s), assumed to be constant, during the crash?

Accepted Answer

Hey everyone. So today we're dealing with the problem about cinematics. So we're being told that there's a 125 kg drone that runs out of fuel at high altitude near the Earth's poles and starts falling towards the earth towards the ice below without any parachutes to help slow down its fall. Now, once it crashes into the ice Or as it crashes into the ice, I should say it has a velocity of 285 km/h and penetrates a depth of 59 cm. With this information. We're being asked to determine the acceleration, the drone experience during the crash, in meters per second squared and as multiples of G, assuming that acceleration is constant. So there's a few things that we need to point out here. The acceleration that we're trying to find is during the crash itself, not actually during the entirety of the fall. So this makes things a little bit easier for us. So let's let's think about this um, with a diagram and let's just draw our so let's just say this is our drone right here, this big ball, that's our drone. Their drone. Now it's coming, it's been falling very far right and finally it comes and hits the snow. Let's just say, this is our snow. Once it hits it goes a distance, it penetrates a distance of 59cm and we know a few other things as well. We know that the velocity, the initial velocity of the drone as it goes into the ice as it goes into the ice, the initial velocity in the Y direction. Because we're only concerned with the vertical motion, it's falling down towards the earth. We're not really considering the horizontal aspects that are in play here were effectively consider them negligent in this case. But the vertical initial velocity as I remember it's during the crash, so as it hits the snow Is 285 km/h. Now we're going to want to convert this to meters per second because we want to find our acceleration in meters per second squared. So let's do that down here. We can convert to 85 km per hour. We can use the conversion factors recalling that. We have 1000 m for every one km. So our kilometers will cancel out. And we can also recall that in one hour We have 3600 seconds. So our hours will also cancel out and we'll have an answer of 79.2 m/s. So, since we are going down into the ground, the object is falling. And if we consider this to be an xy graph, let's say, we can say this direction is positive, why? And this direction is negative Y. So if the velocity is going down this meters per second, if it's going into the ground, that we can also say that the initial velocity is negative 79.2 m per second because it is following a downward motion. Similarly, the uh change in height, the delta Y. This is our delta Y again is in the negative Y direction, so it is negative 59 0.0 centimeters. Again, we want our units or all of our factors to be in S. I. Terms. So we can convert 59 centimeters two m using the conversion factor that there are Uh or in one m there are 100 cm. So our centimeters will cancel out giving us 0.59 centimeter or sorry, 0.59 0.59, Oops, 5 9 m. So if we're going in the negative Y direction, then This means we have a delta Y -0.590 m. We also know that since we're going into a crash, the drone goes 59 cm into the ground and it comes to a halt. So that also means that the final velocity, the final in the Y direction is 0m/s. We don't know how long The drone crashed four, but we are trying to find the acceleration in the Y direction, this is our target. So since we're dealing with cinematics, because we are dealing with speed, displacement and acceleration, we have three of the five values and resolving for one other. So we can use one of our uh uniformly accelerated motion questions because again, we're done dealing with constant acceleration. So we can use one of the uniformly accelerated motion equations, that has these three, these three factors the initial velocity, the displacement and the final velocity. But it doesn't include time because we're not given time. So the formula we could use in this case and I'll write this in blue. Is that the uh, the final why squared does he go to fee initial? What square plus two? A. Why? Multiplied by the displacement. So substituting in our values that we know so far we have zero is equal to and I'm living out our units for the sake of space, 79.2 squared plus two. We don't know a yet. That's what we're solving for into the change In displacement is negative 0.590 cm centimeters rearranging and simplifying. We get that 1.18 A is equal to 6276. And finally we can say that hey is equal to 6200ops, this is 76.6, my bad. 6276.6 divided by 1.18. Leaving us with a final answer of 5.31 times 10 to the 3rd m/s squared. So This is a huge number. Right? And that makes sense. The acceleration as it crashes would be super high because we're traveling through it's coming in at such a high velocity through such a short distance. Only 59 cm. However, we're still not done here. We need to find out this acceleration in terms of, sorry, excuse me. We need to find out this acceleration in terms of G and before we move on I would just like to clarify that our acceleration that we calculated here is Positive but our velocity that we, our initial velocity we mentioned earlier the 79 or negative, 79.2 m/s is negative. And this makes sense because the as the velocity is negative but the acceleration is increasing. This indicates that our object is slowing down because the upward acceleration is sort of halting that downward velocity. Anyways considering this acceleration as a multiple of G, we know that G or the force of acceleration due to gravity is 9.81 centimeters or meters per second squared. And let me write this in. Red Is 9.81 m/s square. So as a multiple of G we need to take a and divided by G, surviving this out. We get 5.31 times 10 to the third into the third meters per second squared, divided by 9.81 times. I'm just gonna write oh actually We're already in our normal state, it's just 9.81 m/s squared. So this means that G Or the acceleration is 542 Gs is 542 times the force of acceleration due to gravity. So looking at our two answer choices, the acceleration experienced as well as the acceleration expressed as a multiple of G. The only answer choice that fits is answer choice B. I hope this helps, and I look forward to seeing you all in the next one.

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