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$\bullet$ A shell is launched at 150 $\mathrm{m} / \mathrm{s} 53^{\circ}$ above the horizontal. When it has reached its highest point, it launches a projectile at a velocity of 100.0 $\mathrm{m} / \mathrm{s} 30.0^{\circ}$ above the horizontal relative to the shell. Find (a) the maximum height the ground that the projectile reaches and (b) its distance from the placewhere the shell was fired to its landing place when it eventually falls back to the ground.

a) 860 $\mathrm{m}$b) 4353.0 $\mathrm{m}$

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

Cornell University

University of Sheffield

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.

08:53

On level ground a shell is…

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so the news coordinates less light off world on by six. Access to the light signed both the shell on the project tied. I have no acceleration in the hollows under directions that they have extra bcu and they would also have the board also experience acceleration due to gravity which points downwards and therefore in the negative my directions that they should be negative 9.8 could make up for a second scrapped. So these are the accelerations experienced by the shell and the project. I'll, as they moved through the air now for the first part, refined the maximum height off the show. So let's first tried the components of velocity that we need. So we not Why is wee not? Scientists are not even on this stuff. Angle off the project tile with respect. Oh, the horizontal axis for X axis. And this is equal to one grating meter per second that this is the value ofthe on the velocity in my direction on final velocity in my direction issue. So this is for the maximum lied because once it reaches the maximum height, it comes to rest for an instance, no, in the y axis so there is no component off velocity in my direction now with the news because the question so one thing to take from here the velocity When I said it comes to rest in the Y X, it means that there is some component of velocity in the XX is in the horizontal direction. So the neck velocity is not cereal. Just the velocity along the wide ejection Macedo at the next night. So yeah, let's continue solving basic questions. So from here we have my minus like not to be equal to negative. We not y squared over twice off really light and this gives So this is a widow Make that they want doing the meet up for a second good and twice off a vibe It is negative 9.8 Meet Douglas seconds. God, this is equal to 7 35 meters. So this is the maximum height off the shelf Now at its maximum height, the shell has VX with physical toe aeronautics or the initial velocity because acceleration along the highest intern direction. I see those velocities now this comes off. This is Ecuador because take our not until an artist of victory decrease that we just use that and we get this company into the 19.3 meet up a second and obviously the final velocity Cedo in the my direction as solid deformed the velocity on the maximum height I zero in the light Addiction, as we discussed here, Now live to the ground. The project projectile has velocity confidence. So this is for the shell. Now we find for the project time so let us to the ground on the project. They will have now velocity components 94 90 minute. Up a second. It is this velocity plus 100 Li double a second call sign 30 degree on DH. This's the velocity off the ground. Ah, respected. The shells are negative. Velocity off the shell with rested too long. So this is it, Cleo 1 76 point nine. Wait up a second on DH. Similar religious until dawn. The next page. They're not Why is staying with him for a second Now we find the maximum height off the project time using these values. So we will use the same question that we used over here. Basically, this a question. Buy it. Why not to be equal toe 7 35 meters. So this gives. Let's knows that the question that we used before so we solve it for the values we have for the project time. So we usually not quite a bit Think for a second. Andrei, get this value, Toby 1 28 Their four lives and being 1 28 meter, that's why not. Which is 7 35 meter. And this gives why, Toby Liquid o eight, sixteen 16 18 years. And this is the maximum height off the project. Pay fun. This is the maximum height off the sent. Now we find the time for the shell to read its maximum height. So he used this is Christian to first find there. Time for the shell. So this Cape Steed to be equal to negative not like over there, because we realize just dedo and the maximum light. And this keeps time, Toby, equal toe, 12.2 seconds. Remember toe news. We're not right for the shell. That is one. Training it up for a second on DH, not for the project. And this is for the project. And so you have to We're finding the time for the shell to retake maximum, right. Give me the strap Project dime closing time. This is also for you guys on This is the ship. Now we find the distance traveled by the shell horizontally during this amount of time. So we used this a question. There is no acceleration. So the second part Half a day C squad and we see it also basically, there should be one. There should be the storm and they cushion with this is zero because acceleration is casino and use me not x for the shell, which is they? Not times we know two times. Go sign Donald Time. Steve, this is a goingto be not this one fifteen 15 meters per second. Andi time is so That is a scientific notice. Three degree and time is 12.2. Sevens is shortly found just now This value and this gives x minus X not still Equador 1100 meter. Now we find the time for the project file footage the ground from the point where it is launched. So it starts from why not? Which is centred. If I were God and ends up at y equals zero listening Is that lying minus Why not is seven texts are negative. 7 $35 on. We really used the same question. Like for the vertical motion. It's in its solve it now. This is 7 35 meter. We not white is 15 seconds. It is 1 50 signed 53 degrees on DH Hope signs of degrees this time here, Linus acceleration half off acceleration, which is 4.9 minute of the second scarred Times Square. So if you um if you bring this negative 7 35 meters to the right and side, you'll see that this is accredited. Cushion off the form X squared. The speaks the sea. The X is your time is make it a 4.9 meters per second squared. The is the not white, so into straightly not why and not this whole Dahlia and seize your positive 7 35 meter Because this comes to the other side, negative becomes positive. Now we saw this quadratic equation on. They get the positive value ofthe time. Toby 18 point for seconds. So when you solve this equation, you'll find tio possible that values so one will be a Let me just write the tenderly question. So so to solve for X use this a question minds for they see overto So you have two solutions. One for class, one for minus. So for the time if you use minors, you'll get a negative answer. So you only pick the positive sign here and sold for time now during this time the project and has a horizontal displacement which is equal to X minus six knot. It is in fact, I'm going to Reno. We're not extinct and we not X for the project file is 1 76 by nine meters per second times the time that we found here and this gives x nine If it's not to the Quito C 255 This means that ex physical drew two through 55 minute of bless X not on X mont. Is they just blind on X? Not is now 1100 meter. This means that X is yes, 1100 meters. So this gives extra V Quinto four thousand three sixteen 16 meter. This is the distance traveled by the project I from the original launch point when it reaches the ground. Now, if the shell doing fires and this is just extra information So if the shell didn't did not fire the project time, it's horizontal drains would be. We could tow this if you solve the questions of the notice physically. One we meet up for a second sign twice. Often, Donati's signed eyes off pretty degree and jeez, 9.8 meter classic, Unsettled and Range. You'll find a great too one side only. So this means that the product tailgates and extra boost when it is fired on DH travels farther than this, as you see.

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