a-cannonball-is-fired-with-an-initial-velocity-of-20-mathrmm-mathrms-and-a-launch-angle-of-45circ-at

Question

A cannonball is fired with an initial velocity of 20 $\mathrm{m} / \mathrm{s}$ and a launch angle of $45^{\circ}$ at a wall 30 $\mathrm{m}$ away. If the cannonball just barely clears the wall, what is the maximum height of the wall?
(A) 5.92 $\mathrm{m}$
(B) 6.34 $\mathrm{m}$
(C) 7.51 $\mathrm{m}$
(D) 8.32 $\mathrm{m}$

Sachin Rao · Accepted Answer

this problem we have given And cannon ball is fired with an initial velocity which is 20 m purse. Again, An angle is 45 degrees at the wall. We just talked him into the way. Yeah, Yeah, like this. We have to find out the height of this wall if can involve just to barely clears the wall. So first of all, we will find that time. So we know that in horizontal direction velocity is V X, which is 20 costs 45 and the stand stable in the general election is 30 m. So time will be called to the stand by velocity. That means activity 20 cost 45 So this time is equal to 20 divided by. So the 30 divided by 20 into costs 45. So this is a call to 2.12 seconds. Now we have to find this height edge Suppose height of Wallace Edge. Now we will use automatic occasion as a is equal to you by t plus half. Hey, by P square, we will apply this can, um, Arctic inclusion in the vertical direction. The vertical displacement is it&#x27;s called to edge initial velocity in the y direction is 20 and two signed 45 time is given. We have fine time. We just 2.12 Okay, plus half acceleration due to gravity is minus 9.8 in 22.12 square. So this is the height of the wall. Now we will solve this. This is equal to 20. And to sign 45 into 2.1 to minus 0.5, multiply with 9.8 multiply was 2.12 square. So this is equal to 7.9 six m. Now, if we check our options, we have given 5.9 to 6.3 to 47.51 So the best auction will be equal to 7.51 ocean. See will be correct Option. Thank you.

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

Ze-Han Lee · Answer

So in this problem, we have a cannibal, which is which is shot at initial velocity. Ah, be notes. Three nautical, 50 meters a second and issuing goes 40 degrees. Okay, so this is the trajectory. And we want to prove that. Ah, suppose there&#x27;s a There&#x27;s a position which is to 20 meters when the show. That&#x27;s ah, right here. The council wars. Ah, because the boys are 30 has height of 30 30 meters. We want to make sure that the cannonball will hit this cause a wall. So, uh, in part A, we can determine the time from the initial position to this. Ah, to this to 20 meters thesis. Okay, so the total time a quote to 20 meters divide by the x component of the initial velocity, which is a 50 times signed. 40 degrees. Okay, sorry. Times call sign 50 times. Call sign 40 degrees. So this gives us 5.74 seconds. All right? And then we can determine the villains in the wind component of the velocity at this at this point. So, uh, why the BYU quo 50 times signed 40 degrees so 50 times signed four degrees gives us the why component about the initial velocity minus g times t right. So the better is the negative 24.15 meters per second. So he tells us that the speed Ah, the white component of the velocity at this point is the negative 24.15 meters a second and we can determine the ah the total displacement allowing the white direction which will be 50 times signed 40 degrees squared minus 24.15 squid thereby to jeep. Okay, so this is the displacement along the Y direction. And we&#x27;re going to say that this equals h equal 22.90 full meters and this is smaller than 30 meters, which is the height off the off the castle walk. So this shows that the cannonball we&#x27;ll keep this a constable and in part B. So we went to the home. How long does it take to get to get to get on the cost of war? So as well as we have found on impart a So that whole time is five point. Sending four seconds. Okay. And Parsi, we want to know. Ah, how many meters were this accountable? Hit the council war. I mean, let me see in part C At what height? Above the base of the wall with the cannonball strike. So that is the one that we&#x27;re on here. Okay, So H equal, pointing to 10.94 meters.

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.

Suzanne W. · Answer

And project was launched at an angle of 30° and lands 20 seconds later at the same as it was launched. What is the initial speed of the projectile? Soap Arcade? Remember the initial speed? Be wise to be not? Why minus G. T. Tears equal to its in seconds? The wise zero the female Y. Is equal to 88 meters per second. So the what is 98 55 Fine of 30°.. Because why is If you&#x27;re not sign of 30? So we&#x27;re going backwards to thank you nine and this is 196 meters per second. What is the maximum altitude? H is equal to the novel? I squared over to Jean. So this is 419 years part C. What is the range? So to find the range you want to find those different X values. So before we can find those different X values we have to find the nite X. Which is being a co sign of 30°, Which is a 169.7 m/s, Then X At 20 seconds is equal to 69.7 times 20 seconds, which is 33 94 m x at 15 seconds, 169.7 times 15. It is 25 50 party calculate the displacement from the point of launch to the position of the trajectory at 15 seconds. So why is equal to 98 times 15 seconds? So it&#x27;s very nice. T minus one hat can t squared And at 15 seconds this is 368 m. So the displacement is 25 50. I had Last 368 jihad.

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.

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