two-cannons-are-fired-from-a-cliff-at-a-height-of-50-m-from-the-ground-cannonball-a-is-fired-horizon

Question

Two cannons are fired from a cliff at a height of 50 m from the ground. Cannonball A is fired horizontally with an initial velocity of 40 m/s. Cannonball B is fired at a launch angle of $60^{\circ}$ with an initial velocity of 80 m/s. Which cannonball will have a greater magnitude of displacement after two seconds?
(A) Cannonball A
(B) Cannonball B
(C) Both cannonballs will have the same displacement.
(D) Cannot be determined

Vishal Gupta · Accepted Answer

hi. In the given problem, two cannonballs ah projected from the same height and the height from which they were projected. He&#x27;s given us 50 meter now one off the cannonball, which is leveled as a is thrown horizontally. Then, on initial speech off you A is equal to 14 m per second and another can involve is projected. You can initially speed UV off 80 meter per second at an angle off 60 degree from the horizontal. No, after a given time interval off 2.0 2nd, we have to find which off the cannonball will be having the more displacement displacement from the initial position. So to find it. First of all, we consider Cannonball he for this cannonball as it is moving horizontally only so it&#x27;s distance traveled horizontally will be found simply using distance. He goes to speed into time and the speed waas 40 m per second at the time given here is 2.0 seconds, so this distance comes out to be empty meter now, for the distance traveled by it vertically means why it for it. We will use second equation of motion which says y a is equal to you. a y means initial velocity of cannon ball a in vertical direction into T plus half GT Square as there was no initial component vertical component. So this is zero less half into 10 for acceleration due to gravity. Again square off to canceling this too. We get 20 meter so it&#x27;s net. Displacement here will come out to B R. A. Is equal to x a square, plus why a square or we can say this is square off 80 plus square off 20 or this is 6400 plus 400 which comes out to be 6800 m. No for another can involve cannonball bait. Its initial horizontal velocity will be given by you be intercourse 60 degree means 80 m per second into one by two for cost 60 degree. So it comes out to be 40 m per second. So horizontal distance traveled by this cannonball also will be equal to will be given by you be X means to speed into time. So this is 14 m per second time again two seconds. So this is also 80 m. But as far as its vertical distance traveled is concerned that will be given by the second equation of motion you b y t plus half g t square. So it comes out to be 80 meter per second into sign 60 degrees into time T minus half into 10 the square off to We have used negative sign as the ball is initially moving in upward direction, for which the gravity will be taken as negative. Now here it becomes 80 into room three by two for science, 60 degrees into minus 20. Nita. So here it becomes 80 Route three minus 20 meter, which comes out to be 118 0.56 Neater so it&#x27;s displacement from initial position will be given by that&#x27;s quite off X B and the squared off y b the tradition and then the square root. So as XB, he&#x27;s having the same value. 80. But why be? Is having much more value than that off by a Hence here, we can say without calculating it, we can conclude that R B is more than are a means. The distance, the total displacement net displacement for cannonball be is more than that. Hey, and this is the answer for this given problems. So here we can see option the his correct Thank you

Kristela Garcia · Answer

in this problem. Two cannons are being shot from a 50 meter cliff, one is being shot at an ankle of 60 degrees at 80 meters per second and one is being shot horizontally at 40 meters per second. And we want to know which one has a greater displacement. Well, if we look at just the angled velocity, it tells us that we have a velocity in the ex direction of 40 meters per second, so it will have the same displacement in the ex direction as the horizontally lunched cannon. So we just need to look for our displacement in the UAE direction. So our displacement in the wind direction can be calculated using Arcana Matic equations, because we&#x27;re only looking the Y direction we need to make sure we&#x27;re all amusing wide values. So our initial velocity and the Y direction for the horizontally launched project hell would be zero, and so our displacement is 1/2 negative. 10 after two seconds uses a displacement of 20 meters, so we&#x27;re now 20 meters lower than where we started, and then same equation. But now we&#x27;re going to use the displacement, the velocity of the wind direction, which is 80 sign of data, which is 60 degrees. So we&#x27;re gonna say Delta y equals my initial velocity again. We&#x27;re only concerned about the Y direction. So all of our all of these values have to be in the UAE direction. So our initial velocity in the UAE direction is 80 sign of 16 times two plus 1/2 negative 10 to square gives us a displacement of 118.6 meters. So we can see that this displacement is going to be much, much greater than our displacement in the UAE direction. So we have a greater displacement by the angled Kenan, which is captain beat.

Ze-Han Lee · Answer

All right. So in this problem, we have a cannonball. Ah, was initial speed 40 meters per second and this cannibal initial aids on the cliff. All right, so the initial speed is vey notes and an angle is 30 degrees the naughtiest 40 meters the second. Okay, so, uh, in part I want to know How long does the cannibal fly fly? Uh, so, uh, we know that initial velocity along the Y axis of anal times signed 30 degrees, right? And ah, suppose on the final destination the velocity along the Y along the Y direction is vf. Why labels the final in a while? It was the wind direction. Then we have equation Renal sign 30 degrees squared minus V f. Why squid Bye bye to G This sequel The final displacement along the Y direction which is negative. 25. Good. Then we can So here we said G quote 10 meters per second squared ok. And we come tonight to me. Why the f y equal? Negative. 30 meters per second. Okay, so, uh ah, the flight time in this case could be Ah, So we have 20. Sorry, we have 40 times. Signed 30 degrees, which is the initial velocity along the Y axis minus g times t equal. Negative 30. Right Then we can sell for this. T and T you pretend that you call five seconds and in part B, we want to know the range of this cannonball. So the initial will also be on X axis is 40 times call sign 30 degrees. All right. So times the total time so that it will be the range of this cannonball. So this gives you Ah 1 73.2 meters. All right. And in part, see well in a trolled Ah ah, the velocity along the y axis and XXX two diagrams. So we know that Ah, the X axis of the velocity alone xxx that&#x27;s not changing the whole process, right? And it is a constant V X simply able to 40 times. Course I 30 degrees and this is 34 points. Six major of the second. Okay. And B, why has expression Ah, 40 hands signed 30 degrees because there is acceleration G minus g t. So this gives you 20 minus 20 meters per second. Okay, so in the first, the plots we showed the relation between the ah T and the VX. So it is just a horizontal line, right? Because the VX is a constant and the value of this horizontal lines 34 when. Six meters per second and four the second graf we showed the relation between the V X and B Y as obedient to you to be Why so five seconds. 12345 and along the whites is so 12 and this is 123 Let&#x27;s say this is 20 meters per second. So the unit is meters a second. Okay, visited this negative negative 20 to 30 and the the uniformed ex excesses at his second. So there&#x27;s a 12345 All right, so initial lost a lot of waxes is 20 and ah, 20 go to to be why become zero? So it is Ah, it is a straight line and won t quit to five byu call 30. Negative. 30. Okay, so this is a relationship to be won t

Nicholas Majtenyi · Answer

question 74 states that it can in this place, at the bottom of a cliff, 61.5 meters high, the cannon is fired straight upward the cannibal Just we just the top of the cliff. Let me just drop this first will do in parts. So todo fue reads of this question really understand what they&#x27;re trying to tell us. But the situation as I understand is it is a cliff here, our first cannonball, a shot from the basic cliff upward and is Max height. It just reaches the top of the cliff. That&#x27;s that first scenario that they&#x27;re talking about. Okay, party started questioning, states it. What is the initial speed of the cannonball Told you this before you go in part because it&#x27;s a little different scenario. So dealing with our cannon being shot directly up. Cannonball being shot directly upward. Excuse me? I&#x27;ll say in the positive. Why direction? I&#x27;m gonna find the initial height of this cannonball. Okay, Mrs Party. So because we&#x27;re getting initial speed and the course we know how high the cliff is. Sorry, we&#x27;re solving for initial speed. And we know how high the Clippers that can magic equation we want to use is such together Final velocity squared equals our initial velocity in my direction squared plus 2 80 So maximum height When the cannibal reaches the cliff the philosophy in the wind direction is zero And know that acceleration due to gravity is negative in this case. But D y is positive because you&#x27;re running from the bottom of the cliff to the top of the club and so is he. Why not? That&#x27;s also positive. So you have. Do you know why squared again? Because JI is negative being represented as to G Do you live? And so our initial velocity, which I was called view Why, michael v dot y Actually, it&#x27;s very a to g the wine. Um because we have the distance in the wind direction. Begin substitute in and we find that the initial velocity to three significant figures is 34.7 meters per second. Okay, great. That&#x27;s special philosophy of the cannibal shot straight up a party is a different scenario. It states that suppose with a second candidate this place at the top of the cliff, the candidates fired horizontally, given me giving its Kimble&#x27;s the same initial speed pounding part, eh? Show that the range of this cannon is the same as a maximum range of the cannon at the base of the cliff. Assume the ground at the base of the cliff is level, although it doesn&#x27;t matter if it&#x27;s level. Okay, so scenario to I&#x27;ll drop blue. Here you have a second cannibal shot from a cannon. Slowly, horizontally, everyone to show that from B the range of cannon to sail right two equals the range. The total distance moved by the cannonball in bomb. The scenario one. So get me a two upto in May of one down below. That&#x27;s that&#x27;s what this question of asking So this new we have initial velocity in the ex direction is what we found in our days. That&#x27;s 34.7 meters per second, so we know the distance in our next direction. It&#x27;s just given by our initial velocity in the extraction times t we know the not next. We don&#x27;t know tea. So is it may be a clue that we need to look at our white component of this equation. De bine equals B not y t again. I&#x27;m not I&#x27;m not gonna drum pluses and minus because I really want to emphasize her. Figure out at the start if I&#x27;m the terms of positive or negative. So they&#x27;re going from the top of the cliff to the bottom and going in the negative wind direction. I mean, my distance will be negative. Maybe not. Why? Well, my initial losses, actually zero. So I don&#x27;t need to worry about the sign for that one. And my acceleration due to gravity goes against my wife coordinate system. So that&#x27;s as we need it as well. They just can&#x27;t sell out, so they could just be positive. That&#x27;s fine. We can get an expression, retire to be simply to G start to G D Y over G. Excuse me to d y over g and all squirted because there&#x27;s a T square turn. Great. So I can now substitute these eyes in just to be very clear, my initial velocity, the extraction times, the square root of two times the height of the cliff over G all these terms you given to us and I find that the total range of the cannonball is 122 0.9 meters. I&#x27;m not gonna worry about my mind of sync. Fix here because I&#x27;m not the reporting that the answer. We&#x27;re looking at a comparison, so you find that the total range of the cannonball when it&#x27;s placed on top of the can, uh, canyon is where the cliffs or I should say, 122.9 meters. Question asks, showed that the range of this is the same that the maximum range of the cannon at the base of the cliff Well, what does that mean when you can shot until the bottom? When it shot straight up, it reaches a maximum height of the cliff and then we&#x27;ll travel back downward. So the range that the cannonball goes through in this new is simply just two times the height two times D y, which I&#x27;m just now realizing that I put my d y in terms of meters per second. So I I apologize for that, and I just racing back simply just as a reminder deal. I was 61.5 meters where I must play my range to the height of the kitchen. So the height of the cliff by two that&#x27;s simply 123 meters. What matches my value for the maximum range of the cliff? So what&#x27;s hired from the top of the cliffs? All right, so, as you see, this is true. The range of the cannibal fired from top of the cliff matches a range of cannibal fire vertically upward at the base that so it&#x27;s

Charles Carter · Answer

soon height that this cannonball is gonna be, uh, at will be at this at the Vertex and the exit position. That the person is a stand to be directly under at the highest point needs to be equal to the X value at the Vertex to the exit after birth. Texas going t minus B over to a It&#x27;s just particular equation. The X value just has the coefficient of one. So be negative one, then divided by an r A value, it&#x27;s two times that message is negative. 64 ada 50 squared or 2500. And so the recent basically the negative Reciprocal. It&#x27;s just gonna be 2500 over 64. Use a calculator, help me out with that decimal. So if that person waits at 39 0.6 to 5, I think, uh, that&#x27;s in feet away from the cannon. That&#x27;s where the cannonball will reach the highest point. Okay. And then plugging that value back in to our equation will give us the next on pipe. So age of 2500 over 64. I&#x27;m just gonna use calculator getting to plug that in, and that value comes out to be 19.53 1 to 5 feet. Okay, thank you very much.

Henrique Saito · Answer

Okay, so we have a cannonball of this question, and it&#x27;s going above a castle wall and into the ground. And we&#x27;re told some information, like the fact that the cannonball shot seven meters above the ground. It makes the initial awesome 37 degree angle with the horizontal and the initial Aussies 40 minutes per second. So first we have to find the peak of the cannonball. So the peak of the cannonball of its trajectory is gonna happen when it&#x27;s vertical velocities equals zero. Okay, so if we use this equation here at the top and we look at Justin vertical components and we set the final vertical velocity to zero, well, that we can solve for the Dell tax or the distance, and so that&#x27;s the peak. So let&#x27;s do that. First things first. Well, the V is gonna be equal to zero, okay? And so we have to sell for V or we have to figure out what v not. Why is vino y Well, that&#x27;s just gonna be cool. To use this triangle, it&#x27;s just gonna be equal to, uh, 40 meters per second times side, 37 degrees. And that&#x27;s gonna be equal to 24.1 meters per second. Cool. Now we have You know why we know that a wise gonna be equal to 9.81 meters per second squared, right, cause that&#x27;s the gravity. And so just like that, we can solve. So we&#x27;ll have Delta X is gonna equal to negative v not squared. Yep. Divided by two A. And you know, technically, acceleration is gonna be negative. Good. So if we do that, we have negative 24.1 squared over two times 9.8 negative. 9.81 And that will give us an answer for the peak of the ball compared to the ground anyways, or compared to the cannibal initial position. And that&#x27;s gonna be equal to 29.5 meters. All right, so he had seven. We get the height of the ball right, because we just have that seven to get to this height. And so we get that the peak height of the ball is going to be equal to 36.5 meters. So there&#x27;s your first answer. Next, we have to figure out where the horizontal distance between the initial starting point of the endpoint. In order to do that well, we need to find out the amount of time it takes for the ball vertically to go up to the peak and then down to the bottom. So let&#x27;s figure out first, this the the time takes the ball to go from zero to the peak. Okay, so let&#x27;s do just that first. Are we gonna do that first while we&#x27;re gonna use this equation and it is the, um it&#x27;s a pretty simple equation. All it is. Just Delta X is equal to V plus V, not over two times T Now get me know that V is going to be zero, right, because the vertically the ball is not gonna be moving at the peak. And so all we gotta do, we know they&#x27;ll tax is going to be, Ah, it&#x27;s gonna be 29.5, and we know we not is going to be 24.1. So we got to do now is sulfur teeth. Right? So we have t is going to be equal to two Delta X over V, not just rearranging this form. Then get into the V. And so that is gonna be able to two times 24.1 divided by V, not which is. Um Oh, sorry. Not 24.12 times 29.5 meters. Divided by 24.1 meters per second. And that will give us a time off 2.45 seconds. OK, so it&#x27;s gonna take to 0.45 seconds for the ball to go from the ground state to speak. So now we gotta figure out the the amount of time it takes the ball to go from the top to the bottom. OK, we&#x27;ll do that with another formula. We have the sort of basic cinematics firmly derive from characters. Delta X equals DV not tea. Plus uh, 1/2 A t squared right? And we know that the V not is going to be zero right? If we look at it strictly from vertical standpoint, because again the vertical velocity of the ball, it is speaking zero so across this part out. And so all we have to do, we know Delta X is going to be 36.5 meters, right? That&#x27;s the height of the ball needs to fall at this point and we know the vertical acceleration. And so we just saw for time and time is gonna be equal to the square root of two times Delta X over except vertical acceleration. And that&#x27;s just equal suit. Square root of two times 36 45 meters, divided by 9.1 meters per second squared. And so our time is going to be 2.73 seconds down. Two words. Everything. Just because that&#x27;s the amount of time takes for the ball to go down. And so we add up these two numbers, we get the total time from the ball at the initial position to the ground is going to be equal to I have 5.18 seconds. Okay, Now that we know this, we can easily find the horizontal distance because the whole result of lawsuit is going to say the same. What&#x27;s it gonna be? Well, it&#x27;s gonna vehicle to V X is gonna equal to 40 meters per second Times co signed 37 degrees, right, and so V X is equal to 31.9 meters per second. So we have velocity constant loss to me. Halftime. In order to find the horizontal distance. What we got to do is multiply those two and that&#x27;s gonna be a 31.9 times 5.18 and we&#x27;ll get a horizontal distance of if we just round it, it&#x27;ll be about 170 meters. So there&#x27;s your answer to this horizontal distance is gonna be 170 meters and then lastly, fr the X and Y components of the velocity. So a two velocity of the cannibal right here, right when it hits the ground, right when it&#x27;s about to hit the ground, we know that the extra lawsuit is gonna be the same. It&#x27;s gonna be 3rd 2 important. I mean, for second to route enter to find the ah vertical velocity. That&#x27;s another pretty simple procedure. Kind of doing a space. But you go already down here. This is gonna be deep, sort of downward. Vertical velocity is just gonna be equal to the initial vertical velocity, plus the vertical acceleration times the time, not time squared. Sorry. Just times time, and that&#x27;s gonna be equal to 9.81 meters per second. Squared times the time it takes to fall down, so to 0.73 seconds and that&#x27;s gonna give us an answer off 27 meters per second downwards and so will make that negative. And so the Y component is going to be negative 27 meters per second. Obviously the X component is still 31.9, that&#x27;s it.

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