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A military helicopter on a training mission is flying horizontally at a speed of 60.0$\mathrm{m} / \mathrm{s}$ when it accidentally drops a bomb(fortunately, not armed) at an elevation of 300 $\mathrm{m.}$ You can ignore air resistance. (a) How much time is required for thebomb to reach the earth? (b) How far does it travel horizontally while falling? (c) Find the horizontal and vertical components of the bomb's velocity just before it strikes the earth. (d) Draw graphs of the horizontal distance vs. time and the vertical distance vs. time for the bomb's motion. (e) If the velocity of the helicopter remains constant, where is the helicopter when the bomb hits the ground?

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a) 7.82 $\mathrm{s}$ $\\$b) 469.2 $\mathrm{m}$$\\$c) $v_{y}=76.64 \mathrm{m} / \mathrm{s}$$\\$d) see graph$\\$e) 300 $\mathrm{m}$

Physics 101 Mechanics

Chapter 3

Motion in a Plane

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Rutgers, The State University of New Jersey

Hope College

University of Sheffield

Lectures

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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.

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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 the initial velocity of the helicopter in the ex direction. We know that this is the X final because there isn't any acceleration in the ex direction and this is equaling 60 0.0 meters per second. Now we know that the V Y find V Y initial rather equals zero meters per second. There isn't any except there isn't any initial velocity in the white direction. And we know that the plane falls from a height of 300 meters. So if we wanted to find the time that it was in the air for part A, we can say that Delta y equals V Y initial t plus 1/2 g t squared. We can save you initial a zero and we can choose downwards to be positive. So we have t equaling the radical two times Delta y divided by G and this is equal in the square root of two times 300 divided by 9.8, and this is giving us a time of 7.82 seconds. So it's in the air for 7.82 seconds before it hits the ground and then we have the port total horizontal displacement of the helicopter during this time interval, the ex initial T plus 1/2 80 squared. We know that this is going to be there because there isn't any acceleration in the extraction. So we have 60 time's a 7.82 and this is going to give us 469.2 meters now Part C is asking us to find the ah components of the final velocity. So v x final we know to be 60 meters per second and then v y final is equal to B y initial plus GT. However, here we're going to say that Yeah, G is negative. So view initial is equals zero and this will be negative 9.8 times 7.82 And this will equal negative 7 36.64 I say negative because this is pointed downwards. So at this point, Ah ah, Munich for second. My apologies. So at this point, we can say that for part d, they're asking us to find Tio show the X versus T grab the X versus time graph and the wide displacement of just time graph. So we have Delta X versus T and this We have tea over X axis and until tax in meters. And this is simply going to be a straight line with a slope of 60 essentially and then for Delta Y versus T. We have brother. If we're saying that there, If we're saying that the point where they are started to fall is there, why initial is there zero? This would mean that their trajectory with somewhat look like this like a parabola. So let's make it a little more like that, so it would essentially be decreasing exponentially. And that's because of the T squared factor in the Delta y equation. And then party is asking us for the distance between the bomb and the helicopter, and we know that the ex velocity of the bomb equals the ex velocity of the helicopter. So after the time interval of 7.82 seconds, the helicopter is 300 meters above with the bomb upon impact, this would be our answer for party. That is the end of the solution. Thank you for watching

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