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?

Video transcript

Hey, everyone. So today we're dealing with the problem about kinematics. 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 kilometers per hour and penetrates a depth of 59 centimeters. With this information, we're being asked to determine the acceleration the drone experienced 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 out our. So let's just say this is our drone right here, this big ball that's our drone. It's a 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 the distance of 59 centimeters. 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 wide direction because we are 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. We're effectively consider them negligent in this case. But the vertical initial velocity as remember it's during the crash. So as it hits the snow is 285 kilometers per hour. 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 2 85 kilometers per hour. We can use the conversion factors. Recalling that we have 1000 m for every one kilometer. 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 per second. 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 Y and this direction is negative Y. So if the velocity is going down this meters per second, if it's going into the ground, then we could 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 si terms. So we can convert 59 centimeters 2 m. Using the conversion factor that there are uh or in 1 m, there are 100 centimeters. So our centimeters will cancel out giving us 0.59 centime 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 of negative 0.590 m, we also know that since we're going into a crash, the drone goes 59 centimeters into the ground and then comes to a halt. So that also means that the final velocity, the final in the wide direction is 0 m per second. We don't know how long the drone crashed four. But we are trying to find the acceleration in the wide direction, this is our target. So since we're dealing with kinematics, because we are dealing with speed displacement and acceleration, we have three of the five values and we're solving for one another. So we can use one of our uh uniformly accelerated motion questions because again, we're done dealing with accel 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 Y squared, does it go to the initial Y squared plus two A? Why multiplied by the displacement? So substituting in our values that we know so far we have zero, it is equal to and I'm leaving 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, which is negative 0.590 centimeters centimeters rearranging and simplifying. We get that 1.18 A is equal to 6276. And finally, we can say that A is equal to 6200. Oops, 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 third meters per second 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 centimeters. 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 Jeep. 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 that we mentioned earlier, the 79 or negative 79.2 m per second 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 uh downward velocity anyways considering this acceleration as a multiple of G, we know that G or the uh 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 per second square. So as a multiple of G, we need to take a and divide it. So writing this out, we get 5.31 times 10 to the third oops into the third meters per second squared divided by 9.81 times. And I'm just gonna write, oh, actually, we're already in our normal state. It's just 9.81 m per second squared. So this means that G or the acceleration is 542. Jeez it 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.