To protect their young in the nest, peregrine falcons will fly...

Question

To protect their young in the nest, peregrine falcons will fly into birds of prey (such as ravens) at high speed. In one such episode, a 600-g falcon flying at 20.0 m/s hit a 1.50-kg raven flying at 9.0 m/s. The falcon hit the raven at right angles to its original path and bounced back at 5.0 m/s. (These figures were estimated by the author as he watched this attack occur in northern New Mexico.) By what angle did the falcon change the raven's direction of motion?

Accepted Answer

Hey everyone welcome back in this problem. We have a computer game where we have a prey trying to protect its young from a predator is we have a duck chasing an eagle and we're giving some information about how they're flying and they're gonna collide perpendicular early. We're asked to find the change in the direction of motion of the eagle. Alright, so the first thing we want to do with a collision problem like this is go ahead and draw a little diagram of what's going on in the system, both before and after the collision can fill in any of the details that we know. So let's take up into the right as positive. Alright, so before the collision we have the duck and we have the ego, we know they're gonna collide perpendicular lee. Okay, so let's have the duck here in red flying to the right and we'll take the eagle here flying down and that's going to allow them to collide perpendicular early, right, perpendicular, lee is at a 90 degree angle the duck and we have the eagle. Okay? And there's a couple different ways that you could draw the duck and the eagle flying, no matter which way you choose, you will get the same result the same answer. Okay? So some of the details might be different in terms of where the positive and negative signs are, but you will get the same answer. So we're gonna take this to be our situation. We're told that the duck is 1.1 kg And that they are traveling 8.9 m/s And they're going to the right. We've chosen right to be a positive X direction. So the velocity of the duck initially is going to be positive 8.9 m/s. Now, for the Eagle, we're told the Eagle is 2.8 kg. A 2.8 kg. And that they're flying 14.8 m per second before the collision. Okay, now we have the ego going down, we've chosen up to be a positive Y direction. So the eagle is actually traveling in the negative direction. So the velocity of the eagle initially is going to be minus 14.8 m per second. Alright, so that's before the collision, we have the duck, we have the eagle. And after the collision we have again the duck, It's gonna have the same mass 1.1 kg, And we're told that he bounces back at 4.8 m/s, so bounces back means he's going to be going to the left now, and because he's going to the left, that's the negative extraction. And so his velocity Velocity of the duck finally is going to be -4.8 m/s And the Eagle, the Eagle is going to have the same mass as before. Okay, 2.8 kg, but we aren't told anything about their final speed or velocity. Okay, and that's what we want to know. We want to know the direction the change in direction of motion. So we need to know some information here about the velocity. Okay, so the change that we need to know the direction of the final velocity to find the change. Alright, so we have a problem like this, we have a collision problem. Let's consider the conservation of momentum. Now, in this case we have momentum in the X direction and in the Y direction. So we're gonna want to consider the conservation of momentum in the X direction and the conservation of momentum in the Y direction. Ok. We have no external forces so we know we can use conservation of momentum. So what does it tell us? It tells us that the momentum in the system in the X direction initially is equal to the momentum in the system of the system. Sorry, in the X direction. After the collision. All right, well, what's in our system? So before the collision we have the duck and we have the ego. Okay, so we're gonna have momentum contribution from each of those. So, the momentum in the system before the collision is going to be equal to the momentum of the duck in the X direction, initially plus the momentum of the ego in the X direction initially. Okay. And after the collision, same thing, we have the duck and we have the eagle. So we're gonna have the momentum of the duck in the X direction finally. And the momentum of the eagle and the extraction finally. Alright, now let's recall momentum momentum is given by mass times velocity. Okay so for each of these terms mass of the duck velocity of the duck in the X direction initially plus mass of the eagle velocity of the eagle and the extraction initially. And on the right hand side we have mass of the duck velocity of the duck and the extraction finally plus mass of the eagle, velocity of the eagle in the extraction. And from this equation we see that this term is velocity of the eagle and the extraction finally that's what we're looking for. Okay that's gonna give us some information about this quantity. The velocity E final. Okay that's gonna last to find that change in direction of motion. Okay so we need to find that velocity so we need to find the X. Component of the velocity. Alright, filling in the information we know. Well let's take a look at our picture, we're talking specifically in the X direction. Okay so we know our duck is moving in the extraction so he's going to have an X momentum. What about our eagle? Are eagles moving straight down? Okay so he's he's not moving side to side. He has no velocity in the extraction. So this term is going to go to zero. Ok. The velocity is going to be zero so that entire term is going to be zero. He does not have an initial X velocity so filling in the rest of the terms with the information, we know the mass of the duck is 1.1 kg Okay, the velocity of the duck initially 8. m/s. Okay, then we have the zero on the right hand side. The mass of the duck again is 1.1 kg times the velocity of the duck in the extraction. Finally, while that's minus 4.8 m per second, the mass of the eagle, All the mass of the Eagle We know is 2.8 kg and we're looking for its x velocity. Alright, so, working this out on the left hand side, we get 9.79 kg meters per second. Okay? We have kilograms times meters per second. So our unit is kilogram meters per second. On the right hand side minus 5.28 again, kilogram meter per second plus 2. kg. That is the velocity of the eagle in the X direction after the collision. All right, we can move this 5.28 kg meter second to the left hand side. We have the same unit so we can add those up. We get 15.7 kg meters per second on the right hand side, we're still left with the 2.8 kg. Times velocity of the eagle in the X direction after the collision and dividing by the 2.8 kg, the unit of kilogram will cancel. Okay, And we're gonna be left with the velocity of the eagle in the X direction. After the collision is going to be equal to 5.38. Okay. And the unit we're left with is meters per second, which is the unit we want for velocity. So that's great. The units check out there. Okay, and this is our x velocity of the ego after the collision. Alright, so we've dealt with the conservation of momentum in the X direction. Let's go now to the y direction. Ok, so we have wide motion. So we have the same conservation of momentum. The momentum of the system in the Y direction initially is equal to the momentum of the system in the Y direction after the collision. Same thing as in the extraction. We have two things. We have our duck and our ego that are both going to contribute to our momentum. So for each of these we have the momentum of the duck and the momentum of the eagle. Okay, in this case we're talking about the Y direction and on the right hand side we're talking about after the collision. Okay, great. Just like in the extraction, the momentum is mass times velocity. Okay, so when we're talking mass times velocity for each of these, we have the mass of the duck velocity of the duck in the Y direction, initially plus the mass of the eagle. The velocity of the eagle in the y direction, initially mass of the duck, velocity of the duck in the Y direction. Finally plus mass of the eagle, velocity of the eagle in the Y direction after the collision. Okay, now this B e y f velocity of the eagle in the Y direction, that's what we're looking for. That's the other component of velocity. We know the X. Component. Now we need to find the Y component. So let's go ahead. I'm just gonna scroll down so we have a little bit more room to right here. All right, so filling in the information we know well, when we talk about the X direction or the Y direction we have our duck, he's moving to the right before the collision. Okay, so he's only got an X velocity. He doesn't have any velocity in the Y direction. Ok, so this term here, this first term it's going to go to zero. The duck is not moving in the Y direction, have no momentum in the Y direction after the collision, he's moving left but it's the same thing. He has an X velocity but not a wide velocity. So this term is also going to go to zero. So we're gonna be left with the momentum of the eagle velocity of the eagle in the Y direction initially is equal to the mass of the eagle. The velocity of the eagle in the Y direction after the collision. Okay, alright, well, the mass is going to cancel. We can divide by the mass of the eagle and we're left with the velocity of the eagle in the y direction After the collision is just gonna equal the velocity of the eagle in the y direction before the collision. Okay, well we know that that's minus 14 by eight m per second. And here it's important to note that When we're dealing with momentum, momentum has a direction. Okay, just like velocity. So these these in the momentum equation our velocity, so we need to include the negative to indicate direction. Okay, we did it in the extraction with the -4.8 and we're going to do it again here, the -14.8. Okay, so this is RVEYF. Alright, so now we have our components of our velocity, so let's dry what we know. We want to know the change of direction. So the eagle initially was flying down. Okay, Now it's flying down. Okay, we know it has its flying down with 14.8 m/s. Okay, But it also has a component to its velocity. To the right, Okay, so it has a component of its velocity to the right? That's given by this x component of the velocity 5.38 m/s. Okay, and so it's actual velocity, we'll be along this vector here. This is the velocity of the eagle after the collision. What we want to know is a change in direction and again its initial velocity was straight down. Its new velocity is along this dotted line. And so the change in direction is going to be this angle data. Alright well, how do we find that angle theta? Well, we can find it using tan. Okay. We know that Tan data. Okay, well that's gonna be the opposite side, divided by the adjacent side. So that's going to be 5.38, Divided by 14.8. So we have data is equal to 10 in verse 5.38 over 14.8. And that's going to give us a data value of 19.98°. Okay. And if we round we will get theta equals 20° and that's our answer. That is a change in direction of the Eagles motion. And that's going to correspond with answer. D Thanks everyone for watching. I hope this video helped see you in the next one.

Key Concepts

Momentum Conservation

Vector Components

Collision Angles

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