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Problem/10 points)moderate wind accelerates pebble over horizontal xy plane with constant acceleration & (6.0i 8.0j)m /52 At time Us. the velocity iS (41 2j)m $...

Question

Problem/10 points)moderate wind accelerates pebble over horizontal xy plane with constant acceleration & (6.0i 8.0j)m /52 At time Us. the velocity iS (41 2j)m $.How much time docs the particle take to be displaced from Om to Sm? Find the velocity of the particle at that time unit-vector notation Jnd magnitude-angle notation

Problem /10 points) moderate wind accelerates pebble over horizontal xy plane with constant acceleration & (6.0i 8.0j)m /52 At time Us. the velocity iS (41 2j)m $. How much time docs the particle take to be displaced from Om to Sm? Find the velocity of the particle at that time unit-vector notation Jnd magnitude-angle notation



Answers

A moderate wind accelerates a smooth pebble over a horizontal $x y$ plane with a constant acceleration $$ \vec{a}=\left(5.00 \mathrm{~m} / \mathrm{s}^{2}\right) \hat{\mathrm{i}}+\left(7.00 \mathrm{~m} / \mathrm{s}^{2}\right) \hat{\mathrm{j}} $$ At time $t=0$, its velocity is $(4.00 \mathrm{~m} / \mathrm{s}) \hat{\mathrm{i}}$. In magnitude-angle notation, what is its velocity when it has been displaced by $12.0 \mathrm{~m}$ parallel to the $x$ axis?

In this problem, we want to find the direction and the magnitude of the velocity after some object has moved 12 m in the X axis with this initial velocity and this acceleration. So let's begin by finding the X. And Y components of velocity. We know that velocity squared is equal to initial velocity plus two times the acceleration times are displacement and we know that displacement in the X axis. So let's use this equation to find our hopes and this should be great. Yeah, let's use this equation to find our ex quantities. So the velocity in the X axis is going to be equal to the square root of the initial velocity in the X axis plus two times the acceleration times the displacement. And we have all this information. We have the initial velocity over here about four square plus two times the acceleration in the X axis, which is five. And then when we are told that the displacement is 12 m along the X axis. So this velocity is going to give us roughly 11 0.7 m per cent. Yeah. Now we cannot use the same equation to find a white component because we don't know the displacement in the y axis and it will probably take a while to solve for the displacement. So it's easy to find the time it took to object to move to this speed in that displacement. So let's use this equation to find that time instead. That's you. So we can say that the displacement in the X. Axis is equal to one half times the velocity in the X axis plus the velocity the final velocity in the X axis. Time is the time. So here we have our time. We can simply solve for that and we find that this is equal to two times a displacement V. X. Access divided by the sum of the initial and final velocities in the X axis. And we have all that information. We know the displacement, we calculated the velocity and we are told the initial velocity. So we simply right for plus 11 point seven that gives us almost 1.5 seconds. So now finding the velocity in the Y axis is very easy. We can simply multiply the acceleration in the y axis times the time. And that acceleration is seven m per second squared that time. This 1.5. So that is going to give us 10 0.5 meters for a second. Okay, now let's find the magnitude of the velocity. We do that by taking the square root of the X component which we found to be 11.7. We square that. How's the white component? 10 point what screen? So the magnitude of the velocity is going to be almost 15 0.7 m per second. Mhm. And finally, to find the angle, we simply use inverse time of the Y component 10.5 over the X component 11.7, which yields an angle, are almost 41 0.9 decrease, and that's our final answer oh!

This Check their full of problem number 18. Um, rude. Giving the exploration of a peple under a moderate wind. Now it is over a horizontal X y plane. So the accelerations given to us in spy I have plus seven j hat. And also we're given that when particle zero, um, philosophy is four I had. So it's purely in the extraction. So important. A some re asking magnitude. Oh, velocity vector. After Havel is displaced 12 meters Harold Hill to, um x x X, which means the displacement pebble undergoes a displacement in the extraction. Right. So then the displacement of the extraction is gonna be a cold to the initial velocity in the extraction times Time plus 1/2 of the acceleration of the extraction. Thomas Times Square, Right. In order to calculate the final the loss of even need to, uh, substitute this information and united you that remember kinetic equation, right? So 12 meters is gonna be equal to the expo. Part of the initial velocity is already four, right? Welcome home into zero. So, for times, time lost 1/2 of the X component of the exploration, which is careful. It's five t squared right. So we have here is basically a quadratic equation, so if you write it a little, a little more pleasant way this is gonna be cool too. She was born five over, Jews to boy by T squared. Plus 40 minus 12 has been equal to zero now, convertible Sold this for time. We're going to need to run across that equation. Radicals Ellis and negative B plus or minus guru of B squared monks for a seats over to A for our case, Exley, Greens, Artie A is to buy our B is the component off the T hear the term for C is gonna be go to negative 12. So then time for us is giving me with negative four. Let's calculate the 1st 1 using the positive here Square root of B squared four squared minus four times. Hey, being 225 times seen, I give it 12 me divided by true times A which is two and 1/2. So then, from here, let me take it to be positive. We find attempt of the 1.53 seconds Let's do the negative life and let me show you comes. The answer comes out to be negative. And we're gonna disregard that because time can't be negative. All of your page the other solution grows as O negative. Four negative four squared minus four times to 100 and 12 divided by two times two and 1/2. From here, we get something negative, something 3.13 seconds. And we're gonna disregard the solution because the time flows forward threat of physically. And now that we don't have time to be 1.5 seconds, we can calculate the final velocity in terms of the initial velocity crossed the exploration times time, right? So the final velocity than the initial waas for I had remembered or I have to. Plus, the exploration is five plus seven g, but I lost seven j half, but reading love replaces by time, which is 1.53 seconds. So from here for I had plus five times one point by three, it's gonna be seven. Seven 0.7 I had, and then while seven times one point by three, it's gonna be 10.7 j hat so that 7.7 plus four in resident seven has lost 10 7 Jihad is our velocity vector after his pebble is displaced 12 meters now we were asked the magnitude of this part. So in order to calculate the magnitude, really tape came the extra phone. It's where, plus the white component square so that I would find a TV 15 point meters per second. Thank you to us. This is the answer to our A in party. We were asked direction off this final lost director. So he's in order to get the direction that's remember Tangent data be wanting with hex. So then the first off the canyon for our case be wise 10.7 when we hexes 11.7, this has been give us our angle. So the angle was gonna be fine. Found here as 46 degrees, four negative 137 point four degrees. So which one are even a pick? You know, tens of the questions we could draw and figure out which quadrant this velocity vector is in. Right? So both necks and Michael implements is conceived here, are positive. So it lives on the first quote. So the last victim of something like this, if you want buying the angle that it makes with the positive X component than our answer is 42.6, right

Okay, we are going to find the velocity, acceleration and speed of her particle. So first let's find the velocity by taking the derivative of are empty. So that's gonna give us a one I. So we'll just write what I. And then plus two T. In the J direction. Our acceleration will be the next derivative which has no I. Component in just two in the J direction. Our speed is our magnitude of our velocity. So we can take our one squared plus r two T square. Okay, so now we're going to sketch our curb because we're going linear in the extraction and quadratic in the UAE it's still going to look like a quadratic. So once we have this and we kind of know it's orientation. Now we're asked to graph the vectors V subzero in ace of zero. So if I put a zero into V, what I get is one I. And so what that looks like is just a vector of one unit directly in that X direction. Now for acceleration, I'll put a zero in. But no matter what T I put in, it's going to be a to J. So for that one that will be two units straight up in that why direction?

We have Our Victor Equals two. Why I get at equals to zero. And our dish vector this is equal to 5.1 cap plus 0.4 Jacob meter at equals to 0.2 seconds. Okay, so in this question we have to determine the average velocity. So average velocity will be given by free vector. This will be equals two. Our victor dash minus our vector divided by delta T. Okay, so substituting values we will get. Our vector is 5.1 uh minus five. Divided by 0.2 icap plus uh 0.4 minus zero, divided by 0.2 Jacob. So from here we get velocity vector equals 25 icap plus 20 Jacob meter per second. So now average acceleration uh sorry, average velocity will be given by more of re vector. This will be equal to one, the root of five square plus 20 square. So from here we get we have race this is equal to 20.616 m per second. Okay, so this is the magnitude of a race Velocity. Okay, so now next we will determine the accelerator angle. So 10 5 will be equals two V. By divided by V. S. That is 20 by five. So from here we get five equals two 75 0.96 fourth degree. Or we can say that five is equals to 76 degrees. Okay, so this is the angle by the of the velocity vector. Okay?


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