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Pelicans tuck their wings and free-fall straight down whendiving for fish. Suppose a pelican starts its dive from aheight of 16.0 $\mathrm{m}$ and cannot change its path once committed. If it takes a fish 0.20 s to perform evasive action,at what minimum height must it spot the pelican to escape?Assume the fish is at the surface of the water.

Hence, the fish must see the bird at minimum height $16.0-12.7=3.3 m$

Physics 101 Mechanics

Chapter 2

Describing Motion: Kinematics in One Dimension

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

University of Washington

Simon Fraser University

Hope College

McMaster University

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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So we have Ah, pelican that's diving down to the water trying to catch a fish And we know that the pelicans dive Ah starts at a high of 16 meters and we're trying to find, uh, how far it can get above the water before it's too late for the fish to react and swim away. And because of this, we also know that our final height is gonna be zero. So are Delta Y. That's why I, minus y zero, is your A minus 16. It's gonna be negative 16 meters because Thea pelicans diving downwards. So it's displacement is negative. Yeah, uh, we can also assume that the initial velocity is zero. Uh, because that's when the pelican starts diving. So it's not moving in the vertical direction before that. We also know that a equals minus G and this case were also assuming that once the pelican starts diving, it's just falling, and it's not flying as to change its vertical acceleration. So we're assuming it's in free fall. And with all this information, we can use this equation. Ah, have initial velocity times, time plus 1/2 y squared. Ah, and we're looking for tea because we're just gonna sell for the time for the total, the total distance first, and then we can factor that in with the fishes reaction time to get our final answer. So we know here. I'll see Negative 16 is our displacement, our initial velocity zero. So that time's gonna go away. If minus 1/2 times 9.8, he squared. And with all this, we can get T squared is around three point 265 and it keeps going. But I'll I'll just round the tea or final answer. Um, 1.81 seconds, Seth time. It takes for the pelican to dive from the beginning to the surface of the water. And we also know that the fishes reaction time is 0.2 seconds. So if we take our 1.81 and we subtract out our 0.2 seconds, we get 1.61 seconds. And this tells us how long the fish has from the pelicans initial dive until it has to start moving and react before it can escape. So we can plug this time back into our initial equation. Eso delta y this one and H e squared and plug in the time. And now, in this case, we're selling for Delta y. So we want to know. Don't know why is zero times 1.61 that goes away, of course, on we have minus 1/2 times 9.8 times are this time 1.61 seconds squared, and this gives us the delta y of minus 12.7 meters and that that's the displacement that the pelican can travel from its initial height of 16 meters before the fish has to react. But we want to know how far above the water the pelican has to get. So we're just gonna say our initial height, 16 meters Ah, minus 12.7 is gonna give us 3.3 meters. And that's the pelicans height above the water. That's how how close can get before the fish doesn't have enough time to react in, swim away

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