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Use the model for projectile motion assuming there no air resistance and32 feet per second Der secondThe quarterback of footballteam releases pass height of feet ab...

Question

Use the model for projectile motion assuming there no air resistance and32 feet per second Der secondThe quarterback of footballteam releases pass height of feet above the playing field, and the football released at &n angle of 35 with the horizontal. Find the speed the football when released: (Round your answer three decima places.)caught bY receivervards directly downfieldheight =feet. The passftsec(b) Find the manmun helght of the football, (Round UoMF answerone decima piace.Find the time

Use the model for projectile motion assuming there no air resistance and 32 feet per second Der second The quarterback of footballteam releases pass height of feet above the playing field, and the football released at &n angle of 35 with the horizontal. Find the speed the football when released: (Round your answer three decima places.) caught bY receiver vards directly downfield height = feet. The pass ftsec (b) Find the manmun helght of the football, (Round UoMF answer one decima piace. Find the time the receiver has reach the proper position after the quarterback releases the football: (Round your answer one decimal place.) Show My Work (Optlonal} Submit Answer [-/2 Points] DETAILS LARCALCET7 12.3.036_ MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the mode for projectile motion assuming there no air resistance 32 feet per second second bombe flving atirude 30,000 feet speed mlle? per hour (see figure) . When should the bomb depression from the plane the target. Round Your Jnswcr two decimal places:) eased hit the target? (Give your answer cerms the What Specd the bomb at the time impact? (Round vour answer munr the nearest whole number ) SuuuU I(



Answers

At time $t,$ a projectile launched with angle of elevation $\alpha$ and initial velocity $v_{0}$ has position $x(t)=\left(v_{0} \cos \alpha\right) t$ and $y(t)=\left(v_{0} \sin \alpha\right) t-\frac{1}{2} g t^{2},$ where $g$ is the acceleration due to gravity. (a) A football player kicks a ball at an angle of $36^{\circ}$ above the ground with an initial velocity of 60 feet per second. Write the parametric equations for the position of the football at time $t$ seconds. Use $g=32 \mathrm{ft} / \mathrm{sec}^{2}$ (b) Graph the path that the football follows. (c) How long does it take for the football to hit the ground? How far is it from the spot where the football player kicked it? (d) What is the maximum height the football reaches during its flight? (e) At what speed is the football traveling 1 second after it was kicked?

All right, We have reached good old problem, number 70 and this is probably gonna be your favorite problem with the whole chapter. Released his mind because we finally get to see some real world application of all these pyramids questions that we've been solving. So here we're giving a a good little physics problem. And it's we're told that path of a projectile is given by these two questions. Got X is equal to the subzero or vino times coast on if they all times t and why's he could h plus B not Santa Times T minus 16 square And here X is gonna be the horizontal distance from where the projectile is launched Toe where it is now And the no is gonna be the initial velocity that the projectile is launched It data is the angle that the projectile was launched T is gonna be time in seconds. Why? I was going to be the height of the projectile at a given time. H is going to be the initial height or the height above the ground that the projectile is launched and recorded. Talk about being on They dont So we're told in this case we have a projector, the baseball hits gets hit by a bat, has given initial velocity or V not of 150 feet per second, and it's launched at an angle of 35 degrees from the horizontal. And it was hit an initial hot three feet. So let's draw little pictures here. So here's our ground. And here's our a little man with a baseball bat and he hits a baseball and it's gonna go flying through the air. So he did it right here in a hot three feet. Lost it like this with a velocity of 150 feet per second initially, and it was an angle fada of 35 degrees from the whores only. This is a situation that we're doing Bill with and part of a ask us to find the Parametric equations that describe the position of the ball as a function of time. You really only have two. Here's Blufgan. These babies, Avi, not they didn't h. And to get are very much in question. So I have X is equal to the note, which is 1 50 come to coast on of 35 which is all times t Now, if you think about this little sickness report here is always gonna be a constant. This 1 50 coast on 35 Mr Costin, and lets that calculator quick like clearing the right mood. That's about 1 22 point. Just keep him. I just got this cup Sitting here is not a variable. It's all just a constant Cumpsty. And now he's gonna equal H, which is three plus one. They sign of 35 degrees times t my 16 hey, squared. So there's our set of parametric equations that describe possession of the ball is a function of time. And I think about this, which Collins has given us his forgiven time t go back to her picture here. Just gonna give us the X and Y coordinates. If we assume that this is the Y Axis, this is the X axis, but the origin being right to the point on the ground directly below where the volume was first hit and Part B, we wanted to describe the ball's position after 12 and three seconds and locate Those solutions are curved, so basically we won't know for T equals one second two seconds three seconds. Where is the ball? What's his coordinates? X and y. So we've got no, I do. Here's plug in the values of team and get out. Um X and Y coordinates next equals 1 22.9 times T times one just 1 20 Do that. Times two for tea is to 45.7 and then times three iss 3 68.6 How for while we've got three waas 1 50 Signed. 35 terms T rules one. Not now. Vice 16 once. Where in that? 73. What? Oh, around to the nearest. And then we'll change that to take one too. Again t to their get. Why 111 one And finally for t equals three seconds. Yeah. 1 17 What? One. And now it's graph that Yes, I get the gas going bear y axis and our X axis. So we've got Let's call this 50 could be 100 1 50 200 to 50 300 3 50 400. Thanks. And er Oh, this 25 50 75 100 1 25 1 50 one's head 200. So let's just bought this point. You've got 1 22.9 Here. 73. Yeah. 2 45.7 Get 1 11 should be right there. And 3 68 the year. 1 17 for one, which is not much higher. So we're on right there. And so this is the path for Bo gonna be a problem. Which now what we expected, I guess. Really. This shooting girl with zero? This is goingto Michael's three feet when X equals zero. All right, so there's part beef part c asked. How long is the ball in flight? So how do we figure that out? So we won't know this way. So this Paul is gonna come back down, gonna hit the ground somewhere here. I don't know how long that takes. So if wow, when the history Graham's gonna be zero. So really, we need to solve this equation here and figure out When? What Time T that while legal Zero. So three. So we're going to hear zero y zero three plus 1 50 It's on 35. Freeze, Humpty. My 16 t squared. Let's rewrite that just to be a little. We're clear. It's perfect. Put this in the quadratic equation to solve this. All right, So what? Values of tea? Obviously, one of them is gonna be close to zero, but not quite zero. Because we know Tom zero. Why was actually three. So let's see, we got the quadratic equation, right? Say to use it to negative B. This is our B term native 1 50 signed. 35 degrees plus or minus the square root of B squared 1 50 Sign 35 Reese Hall Square minus for Time's a his native 16 Tom. See, which is three over to a two and a was negative 16. So I'm gonna pose a video here and take just a second to run this big thing through a handy dandy calculator. All right, coming back here. We're seeing it will be solved. This for the positive solution we get. T is equal. Negative 0.3 seconds. Obviously, this ball is in the air a little longer. Point over three seconds. What this is is saying that and I can't have native times over. This is just extremist altogether. But what this is saying is that when Tom Mickle zero, you're three feet. So it just before that, if you were a girl extend this curve out that you get on the ground just a little bit prior to zero. Is all that saying That's just extreme solution. So, really, the ball's in the air for 5.4 seconds. And the second part of part C asked, What's the total horizontal distances? Terrible's what we know that X, This equation X that we've found is the horizontal distance. So we can just plug in this value of tea into who are equation for X. And that was 1 22.9 right? Yes, 1 20 I have a 5.4 seconds, and that is going to take five or 600 63.66 feet. So that's the horizontal distance when it hits the ground. Finally, hard day. Oh, uh, another thing about what part see we will see is that, um, consistent with the graph. This 600 feet, man, Yeah, let's say it's close. Kind of pulled this down a little much, you know, if this was really a true probable, that would be something like that. So let's be 500 5600 6 63 Yeah, it's pretty close. That's just a rough sketch, and I say That's about about Rod. So 663.66 feet is where the ball is gonna hit the ground. And Part Day says, use the graft to describe something about the path of the baseball that might be of interest to the player who hit the ball so we won't know how. What. The baseball player. But I wouldn't think so. Let's Paul is a video here, and let's go look up and see what the average length of a baseball field is. Back in a sec. Okay, so we're back now, and I found some interesting information that we might I want to tell our baseball player about. So let's look at Fenway Park, which is the home of the Boston Red Sox. If you're familiar of baseball, this is the green monster out in left field. They have this really huge wall. Let's go green because it's the Green Monster. It's really big tone wall at it. Left field this 37.2 feet tall, and the reason it's so tall is because Fenway Park Field is actually a little bit shorter than most fields. It's only from home plate to the left field wall is only 310 feet, and that's still pretty good ways. And I know I could hit a ball over the fence, but I guess these MLB sluggers probably good. So they made the war really tall. Compensate for this relatively short distance. No, this baseball player. With these initial conditions, let's see if this baseball player would have hit a home run, so we won't know what's the hot that 300 10 feet and happen. We find that out. Let's see well, at X equals 310 feet. What would be t? So we've got an equation for X X equals 1 22.9 roughly empty. So we're gonna antennas x 1 22.90 That's gonna tell us that T is equal to you. 3 10 divided by 1 22 or not. That's two point 52 seconds. So that means if this ball were to go over the fence, it would cross the top of the fence. You would say like this. And across the top of the fence. 2.52 seconds after it left the bat. Well, 2.52 seconds. How high is the ball and we can. We've got an equation for why they get us the height of the balls. Let's go back up here. Copy that back down. Why is equal to three plus 1 50 son, 135 degrees times t 16 t squared that we'll check that. Yeah. So now let's believe this value of tea into this equation for a while to see how the ball was at that time. 50 son 1 35 degrees times 2452 seconds. My 16 times 2.52 seconds squared, and I'll pause again and we'll see what that is. I have to run through the calculator. So after running this through the calculator, I've got some good news for our baseball player, because at that particular instance, in time, our baseball is 168.7 feet above the ground. And so, with our green monster being only 37 point to you, the that's definitely greater than 37.2 feet and good news to our baseball player. He has made a oh broad open door. This problem. I think this is a top, a problem that's really big for people who were looking to pay his assistant. Engineers enjoy this type of problem. May be looking at that profession because I'm an engineering student and I really enjoyed doing problems like this. I hope you did too.

So the Cuban christian is a hopeless new york city plus a by two T spare because to etch. And the table presented is as follows tea time and its height in feet. The time is one country and high forgiveness 84-136-10 1 56. So just write down the equation at respective time because to one A chocolate no one place it's too awful and experience what Because to 84 equals two actual plus Neil two plus a way to despair is born. It was 2136 And he was three. A topless video three less able to Of nine is 1 56. They know this as a question one equation to an equation three respectively. You know Question of 2 -3, you're one plus subjecting this side. He went to three equals 2 52 and question 3- stick person too. This can be lieutenants you want plus able to 4 -59 minutes for this fight. So this is 21 56 -136. Let this big question for And this big question. So the question 5- situation but now will be a right to you will be canceled on As it is same ever to back at two years 20-52 For a finally themselves to 32 feet force again square. Mhm. Since we have known A. So by the question of four you can see he was two into three In 23 plus This video quantity was 52. So we a little bit particular minus A into 3 2. And a value we have calculated just about Here is -32 50 to -32. Into the way to Which is 50 to plus 48. Or we can say 100 1 300 ft or second. So the US 100 ft per cent. And lastly that term Actually. So from the question one we can say A topless real one plus a white two of one was 84. We have known the two values. We always 50 100 and he is minus attitude. Yeah. and one is 84 I took plus this quantities 100 16 was 34. This is a joke. Last 54. Close to 84. And these councils. How So experience? Finally, only 05. So he had out of the answers, you know, Minor strategy to quit for a second spirit. Mhm. We not 100 ft was in And it's not this cedar city. So this is our

All right, So this question deals with vertical motion with gravity and acceleration due to gravity. So this is the equation that represents that age of T equals 1/2 a T squared plus B T plus age. They give you a data chart with some data collections. And so the first relationship is 1 84 which means that at Tom one, this projectile is 84 feet near. I also give you two and 1 36 which tells me that at time to its 136 feet in the air. And then finally they give you three and 1 56 that a time. Three. It's 156 feet in the air. Your ex coordinates in these ordered pairs are your T values, and your y coordinate is your h of tea. So we're gonna substitute those in to create our system of three equations. So if I start with this first point, I'm going to have ah, 1/2 a time to one square. Excuse me. I'm going to drop the zeros and just say v times one forwards sake of time and then H now if I clean that up that's gonna equal 1/2 of a plus B plus age. And then it equals the Y value, which is 84 for this one. If I put this one in this time, I have 1/2 a times to square was V Times two was age, which is 1/2 of four, which would be to a plus two b plus h equals the Y value of 1 36 And then finally, this point here is gonna be 1/2 a times three square was being times three plus age, which will give me half of nine or not haves a plus three b plus age equals 156. And we've created our system of three equations, three variables and three equations. And so now we need to start the process to solve that system. So I'm going to start with the first and second equations, so I have 1/2 a plus. The close H equals 84 paired with to a plus. To be plus age equals 1 36 I could immediately subtract those because my h is air the same. And so that gives me negative three have a monos v equals negative. 52. All right, We'll do that again, this time with the first and the last. So I have 1/2 a plus. V plus age equals 84. Repairing that one with the non hands A plus three v plus age equals 1 56 Since the h is air, the same on this case is well, can immediately subtract. This is gonna give me negative for a monness to be equals Negative 72. This has reduced my system now into a two variable system. So we're gonna put those two together. So we have negative for a I'm honest to be equals negative 72. If I multiplied this equation by two before I bring it down That way my fees will match up. So I'm gonna have negative three a modest to be equals negative 104. And so then subtracting is going to give me negative a equal to 32 and so a equals negative. 32. Once you get one of the variables plugged that into one of those to bury league rations, we have negative for a minus to B equals negative 72. So negative forward times. Negative 32. Multiply that and then subtracted over. You get negative to V equals negative 200 and so v equals 100. Now that I know A and B use one of your original equations I'm gonna use to a plus two V plus age equals 1 36 and plug in your A intervene so two times negative 32 plus two times 100 plus h equals 1 36 Multiply and add Move it to the you're gonna get 1 36 plus h equals 1 36 And so, if you subtract h zero So our equation then, um are what they asked us for. Here the acceleration is negative. 32 The velocity and Tom zero is 100 and the height at Tom zero is zero from there are three unknown quantities.

Even equation is H. Because the right to the squid plus we not be let's teach you so the people of time and how it is given deep and it's that is in feet straight So 123 And the height is bacteria. 36 or d. n. Yeah so the system of the present Equals to one. It will be a two plus we want less. A very too One goes to 36. This is a question one. The constitute Petroplus real tools. Yes A. By two. Sports was to what the. This is a question too And equals 2 3. It's too less you're three. Let's get right to the spirits night these values. Yeah question for solving first question two minus the question what? So if we do it we get video one less By 2 3. It was 2 4. Let me question the big question for. And situation 3- equation of two. It will be real. One place a right to of 5. -4 is five. And this gullibility minus 28. This is a question I question fight minus situation for now. Well the video will be cancelled and we will be remaining with a 5-4 to his minus strategy. So it will be -32 m 1st. They can despair now since it is known. Question of Yeah three question of ford both is real one less. Yes he right to 34 So here you can be obtained. No you can be region is for minors three ways to 10s of a. or 4 -3. Right two times off minus taxes. These values 48 Support plus 48 Which is 52 military force again. And the last value we have to find is that you. So for this equation one Any question one is true. Yes We know one last year right to he wants to 36. The actual plus the u. s. 52. If I two is minus of 36 x two. Yeah. was to 36 A hopeless There's a 50 to- of 18. Close to 36. A two plus 26 26. This is canceled out. And finally actually zero. It was a moment. So these three are our answers joe zero m. The video has two m/s, an exploration iCO s minus 22 m per second squared.


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