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Question Aand C involve separate contextsYou walk 30 m north and then 20 m northwest. How far and in what direction do you need to walk to get back to where you sta...

Question

Question Aand C involve separate contextsYou walk 30 m north and then 20 m northwest. How far and in what direction do you need to walk to get back to where you started?You throw a ball directly at the ground with initial speed v The ball bounces and when you catch it; the speed is v/2 Deterine the magnitude of the change in velocity:A colleague of yours has calculated the position for an object with initial speed Vt to be the following finction of time: x(t) What are reasonable units for the qu

Question A and C involve separate contexts You walk 30 m north and then 20 m northwest. How far and in what direction do you need to walk to get back to where you started? You throw a ball directly at the ground with initial speed v The ball bounces and when you catch it; the speed is v/2 Deterine the magnitude of the change in velocity: A colleague of yours has calculated the position for an object with initial speed Vt to be the following finction of time: x(t) What are reasonable units for the quantity b?



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At a given instant the football player at $A$ throws a football $C$ with a velocity of $20 \mathrm{m} / \mathrm{s}$ in the direction shown. Determine the constant speed at which the player at $B$ must run so that he can catch the football at the same elevation at which it was thrown. Also calculate the relative velocity and relative acceleration of the football with respect to $B$ at the instant the catch is made. Player $B$ is $15 \mathrm{m}$ away from $A$ when $A$ starts to throw the football.

So we're given this equation of a bowl rolling down in a straight line and I'm just gonna be right. This is except T because it's the same thing. It's a function of time. And the first part is wondering what's the position of the ball of various times? So for ex of one second, we're gonna plug in for tea. So two stays the same, 3.6 multiplied by one, uh, plus 1.1 times what squared. And this is gonna equal, uh, negative 0.5 meters, uh, and then next part again, just plug in two seconds. So we have 2.0, you 0.6 plug in to, and this comes out to be 0.8 meters and then plug in three seconds. Class one point on three squared and this unequal 1.1 meters. Now, for the second part, we wanted the average velocity over this interval from one second, 23 seconds, three seconds. And this Delta V, what I'm gonna call is Delta X over Delta T. And so this is gonna equal Delta X will we want Exit three, which is 1.1 meter minus one minus 0.5 meters and then we'll divide by the time interval. Three seconds minus one second on this comes out to be 10.8 meters per second. For the last part, we want to know that instantaneous velocity a two seconds of three seconds and so I can get this velocity function from the position function by taking the derivative. So, uh, Viv T it's gonna equal d x t beachy. Ah. And so the constant was away and we'd have minus 3.6. Plus, uh, 1.1 times two is 2.2 p. And then to find the to plug it in again, So plug in two seconds and this equals 0.8 meters per second and three seconds, uh, equal, and we'll plug in three. This equals three meters per second.

The problem is saying let there be two boys both is at height H his work his catch one throws the ball outside with me I and one with now inside with me. So what is that Time when this both will strike. So let it be t. one and it strikes let it with people. So by observation we know that the one will be Less than T. two and given her and even via velocity it will be hide and G will be let's listen you to gravity and he will be time. So yes we right the question of motion patient of motion. Mhm. The second question There are three questions. The second questions that we study in question of most channels as equals two the beauty plus half a teaspoon. So we'll use this formula for time calculation for this problem that will because two USB I the initial t minus half of G. T. Square. Let's listen due to gravity is G. Just here in this political question to which comes to me I. T minus GTs. Birth calls to Gt squared minus fruits me I. T. Plus to act with crystal europe. So this is quadratic question now since this is quadratic equation, we know roots 22 Those 20 cooks will be minus knee plus minus B squared minus four A. C. Back. So this is a formula for you two to minus two. Even in this case will be we will subtract one value. So this will be cancelled and we will only remain with who signs off route. We square minus for a C. Upon to which will be with over B squared minus four is upon it. So comparing in this equation, what is our B this is it, This always be and this is sick. The sign is also included in quadratic question. So The two dynasties Stephen will be Mhm Yeah, which is you don't say gee to her piece. Various Yeah, For me I spared -4 and took two G. According to S. G into Yeah, see we just do it so we can take the outside to all over we spare minus two G. H upon. So this will be our final solution of part of it. Mhm But but mhm we have a spare managed to be age upon. Mhm Now for the second part yes for the second but it is asking Mhm velocity, Mhm Yeah. So this can be derived from the second question we square because these vehicles to use purpose two years, we know this formula this very close to use plus who is? Yes. So in this case this is we are and a G. So we can see that we have here the independent of direction. So we are building well over the ice Burtless two of G. H. Boy, both the balls since exploration is same move the books. So for the third part there will be two cases are you asking how hard how five of five will be involved. So the question is a bit land here one we will go step by step so for the case yeah elected. This is the work and this is what was the I don world. It will lead maximum map. Yeah maximum will be spirit will visit all the time time. This much time then we uh we do not get it as time even so even we can calculate from the formula Because you lost 80 For him, he is zero and yes so G is negative and P. So people still we are ready so for up to this time what will be sure? Yeah the distance will be simply two times its lesson times it is going downward, it is going upward. So it is exciting with GT it is exciting, it is expressing with minus since it is moving upwards so the strands will be simply who G. Mm but he lives in the top right now. No for the second place for the second case when both wall starts falling downward then it's isolation will be known become positive and this will also be positive. Now distance will be fixed which will be two G. T. Critical the system critical welding. So too cheap. Yeah, this is so for the last part I had done a mistake will again calculate and the mistake was the formula mhm. This the stance is how GTs were not the people's with one minutes. And so this is how GT square to similar concept, one is going upward and one is going downwards so what he calls to okay the B. I. G. The time till this upward becomes zero. We have described this thing. So this is the required time since me of what is zero. So it will be simply this formula peaceful time last time last. So for first case one yes one went these lessons really elevated in case too. We will be sorry, they will be greater than the blog for this case the distance will be become constant because both will like it has let's suppose of the time it has reached here, it starts falling down since both are in the same direction and same G. Is presented. So for this the distance will become this distance will become constantly because become constant and what will be the constant value. This will be hard for gov T. Critical critical is until it's reached. Half of GOP critical was the ICT by G holy spirit which is half jean. The ice bear upon despair into two because both In one is going up or down and people will be more than cases. This is two balls. So that's where we are multiplying it by two simply it will win. We swear by we are super veggie. This is the further he spoke. Yes. Okay

Okay, So in this problem, we have a function that describes the position of a particle. The function in his ex if course five D minus Stan T Square. Okay, so the first item of the problem, we need to discover the initial velocity, the initial position and the acceleration of this particle. Since this is ah, second degree function, we know that this should be accelerated movement. And we know that the generic immigration that describes, uh, position of a particle is x zero bolos V zero t plus a divided by two T square. Okay, so let's look to the initial position. The initial position is when the time equals zero. So sporting T equals zero. We're going simply have initial position off zero meters. And what about the initial velocity? The initial velocity? We can come there. That's weird. In here we have X equals five key minus stand key square. So if we look here, we see that the zeroes needs to be five. So the initial velocity is just five meters for a second. What about the separation? Do the same thing. We just compare the genetic function we have to the position with the one we have in this particular problem. So Dan minus Stan needs to be close to a divided by two, which means that a is going to be minus trying t meters per second squared. This is the answer to the first item. The second item. We need to do a lot of dysfunction. Okay, let's put a function here. We have Let's see, ex grows five D minus Dan de square, and we need to blot the graph between the Times T CO zero and T Coast through. So thinks this is a second degree function. We know that the behavior of dysfunction of this graph should be a horrible and we just need to discover what is going to be the position and t because two seconds. Let's find this. We have to position it's gross five times, two miners 10 times for So this is just minus dirty minor starting in the position. Okay, so let's see. So we need to remake his graph because we're not gonna be able to a lot this graph in minus dirty with the X is like this. So let's see, That's pretty exes. Uh, here we know this is a second degree function and dysfunction has aken captivity negative because off the constant follows the teeth square. So we know that this function begins in zero. It grows up in two minus dirty. So we're going to have a lot like this. This is the position the plot in T equals two seconds. In the third item, we need to discover the average velocity between the time deco zero anti equals one. So let's see average. The last city is just the displacement divided by the difference in time difference. In time. We already have. It's just one second and the displacement? Well, let's see. We just need to discover what is the final position and t close one and the position Antico zero. We already know. So the position and t it goes one going to be five times one minus 10 times one. This is simply minus five. So the average velocity in this interval is just minus five minus. Mine is you know. So the answer to the third item is the average speed, the average velocity. I want to be minus five meters per second in the last item. We need to discover the average speed between worm into seconds. So let's do the same thing again. We already know the position. Yeah, T equals one. But what is the position and the equals? Two seconds. So the position you're going to be two. Sorry. Five times to minus 10 times four. So this is equal to 30 minus dirty meters. So the average velocity, it's going to be attacks divided by daughter T. This is simply minor. Sturdy, minus minus five. Just going to come positive, divided by one. So this is just minus 25 meters per seconds. That's different. Arrested to the problem. Thanks for watching.

In this problem were given an initial velocity of twenty meters per second. An acceleration of the form minus big C times T that it takes eight seconds until the object stops. And then obviously when the object stops, it will have a final velocity of zero meters per second. You are asked to find C. To do this, we need to integrate this form of exploration to get fifty. So r A V is equal to the integral of bay, so minus C t dt. And then we have a re not now moving the vino Teo sign. I've seen his fee not is equal to minus eight people in the CIA funeral. Any girl of T g t, which is t squared over to you. And now I can plug in values for tea and he might be not, and then calculate pixie so we know negative twenty. That's his being might be not is equal to negative big C Times t squared over to in this case T Square to sixty four. Since tea is eight. So sixty four over too calculate for see, I get that C is equal to zero point six to five meters per second cube. We're giving these units of the problem, and that's the answer party for part B. We're trying to find the distance traveled during the trip, so a sense is equal to negative. C Times T squared over two plus B. Not we confined except tea. By integrating this so X is equal to negative C over too times the integral of T Square DT plus the nottie. Plus it's not so in this step, I pulled the negative c or two outside the integral. So I just have the year old teeth for Aditi. I integrated. Just be not which all does is put a tea there and then we also our excellent here and now we need to carry out the integration So I get t cubed over three. Must be naughty plus X. Not so we want the distance traveled. And so really, we want X minus x non. We don't know what x not ISS, but we just know that x minus X not is the distance traveled during this trip? Now we figured out what our see value was, and so we can plug it and we know what T s t is. a seconds. We know what the knot is. We know what he is. And I mean, with Exxon over. So we have everything we need to solve this. And when you do this out of the calculator, you get the ex. My sex not is one hundred six point seven five two meters, which is the distance traveled over. The trip from time is equal to zero seconds to time is equal a seconds. And so this is the final answer.


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