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3.22 00 At t = 0 a rock is projected from ground level with a speed of 15.0 m/s and at an angle of 53.08 above the horizontal. Neglect air resistance At what two ti...

Question

3.22 00 At t = 0 a rock is projected from ground level with a speed of 15.0 m/s and at an angle of 53.08 above the horizontal. Neglect air resistance At what two times t is the rock 5.00 m above the ground? At each of these (WO times, what are the horizontal and vertical compo- nents of the velocity of the rock? Lel Vox and Voy be in the positive x- and y-directions, respectively:

3.22 00 At t = 0 a rock is projected from ground level with a speed of 15.0 m/s and at an angle of 53.08 above the horizontal. Neglect air resistance At what two times t is the rock 5.00 m above the ground? At each of these (WO times, what are the horizontal and vertical compo- nents of the velocity of the rock? Lel Vox and Voy be in the positive x- and y-directions, respectively:



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At $t=0$ a rock is projected from ground level with a speed of $15.0 \mathrm{~m} / \mathrm{s}$ and at an angle of $53.0^{\circ}$ above the horizontal. Neglect air resistance. At what two times $t$ is the rock $5.00 \mathrm{~m}$ above the ground? At each of these two times, what are the horizontal and vertical components of the velocity of the rock? Let $v_{0 x}$ and $v_{0 y}$ be in the positive $x$ - and $y$ -directions, respectively.

A man extent on the roof, off 15 m, Billy and through the rock This publicity Can we meet up for a second at Angulo? 30? Really have up the hard gentle You can ignore that. A distance calculate question Mark the maximum height. Have a little magnitude up Felicity just before it's priceless. The harder, gentle please foraging territory from the base of the building. Me draw extreme the estate and me by picking up Let it start solving it. Consider this is Toby origin. So we will. Major Alderdice. Sensible, Respectable. Now, first Gallipoli, initial velocity and off accepts is and why I accepted. This will be we not. What's so bad. Probably not. Is given Herbie course off perfectly. It becomes don't be five point to meet the second along by direction. In each of validity we not so I know that is 30. Sign off for tea. Movie 16.3. Meet up our second in the heart genital direction. Acceleration is zero in the vertical direction. Acceleration is minus T so that concerned we have a plate. No question about it at maximum height B. But I believe you. A later condition on a vehicle we might be not. It will be not by this square study. Be very square. Be not by its square my point. Who if I substitute there Really? If you don't, do you not buy it? Major 16 points today with respect no minus 9.8. So this is really you will get have been fined 6 m So hide of that room from the roof of the Tavaris 13.6 m No be part Find the validity for acceptance and by exes in the extraction by the city debates constant because acceleration is zero of the x expert toe B not X that 25.2 m per second Because in horror genital direction acceleration is you don't No bi bi bi bi initial Absolutely sorry Acceleration it minus 9.8 m per second squared big respect toe X displacement in the wider extended minus 15 m and in each of validity of you know along by exited 16 point 3 m per second. Now apply the equation. The vice quit will be be not vice square unless who a by and why minus why not substituting the value and solve it the right you will get a rooftop. This value is given 16.3 Holy Spirit minus 9.8 minus IPI. But it would be completely pointed Wheat up our second, but will be in downward direction so we can write minus 23 points of it. Meet that person. No, she we have to calculate the range. You can call it the read be required that time taking to reach the ground. So, B by expecto we not by and that's a boy in tow. He is that I'm taken to reach the ground. This value is 23 points of it we not by its 16 point three that is positive. He is 9.8. So from here you will get 41 beautiful your ticket No rain Huma calculate axis called M minus X not is the rage that will be initial relatively along XX is into type B E X series, you know, Remember it if you want to write human right X in tow piece where? What? X zero b not x is 25.2. Time picking is four point. Do it on this bed with zero so range you will get one dealer perimeter in the party. I forget to calculate one thing you may calculate here, Manu. I'm gonna flipping here, so don't get confused. Magnitude off validity. Lending human wine. White ruled up. Be excess. Quick. Let me buy square. The exists 5.2 bx is minus 23.7 Foley square on it will be equal toe. People want six, neither person. Yeah. So this is a magnitude off balance city lending? No. We end up next. We approved. Wrote the Grab Expedia Expedia up. Would we had eight line? Because in the heart genital direction Well, the city's constant acceleration zero Why pick it up and having acceleration in Italy acceleration then need a leader, traditions and acceleration. So it really be like this Relatively b X. It's constant. So it will be a little time axis and be right. That son for this problem things by watching it

For this problem on the topic of motion. In two dimensions, We are told that a rock is thrown from a 15 m building with a speed of 30 m/s at an angle of 33° above the horizontal. We want to find the maximum height above the roof that the rock will reach its speed just before it strikes the ground. The horizontal range from the base of the building that the rock will strike the ground. And we want to draw graphs for X versus T. Why versus T. V, X versus T. And B. Y versus T. Now we'll take the region of coordinates of the roof and let the positive Y. Direction be upward and the positive X. Direction be to the right. The rock moves in projectile motion with a X equal to zero and a Y equal to minus G. We can then set up constant acceleration equation for the X and Y components of the motion. Firstly, the initial velocity has X and Y components. We not cosign Alpha not and we not sign Alpha not, respectively, which is 25.2 m per 2nd and 16.3 m per second respectively. So firstly for part A to find the maximum height, we know that at this point V Y Must equal to zero. And we can use the equation. The y squared is equal to Vinod Y squared less to a Y into Y minus Why not? So we can rearrange this equation and solve for its displacement at the maximum height. Why minus? Why not? Is the speed at the maximum height B Y squared? Mind its initial why component of its speed, we're not Y squared Over two times the vertical acceleration to AY. And so this is zero at the maximum height minus V, not Y 16.3 m per second squared, Divided by two times -9.8 m/km2, which is G. And so calculating, we get the maximum height that the stone will reach of Iraq will reach other 13.6 m for part B. We want to find the speed of the rock just before it strikes the ground. Now we'll find the velocity by solving for X and Y components and so it's X component would remain the same. The X is equal to the not X. This is not affected by gravity and so the ball strikes the ground at a X. Component of speed 25.2 m per second since the acceleration in the X direction A X. Is equal to zero. Now we need to find the Y component of the velocity. So we'll use the equation. The Y squared is equal to we not Y squared plus to a Y. Into why minus why not? And so we get V. Y. To be minus the square root of the not peanut, Y squared plus to a Y into y minus. Why not? We take the negative route because the at the ground the rock is traveling downward and so this is minus the square root of the initial speed. 16 three m/s squared plus To into -9.8 meters a square second multiplied by the vertical displacement minus 15 m. This gives us the why component of the speed as the balls or the rock strikes the ground to b minus 23 .7 m/s. And so therefore the magnitude of this velocity V is the square root of the sum of squares of the X and Y components, the X squared plus b, Y squared. This is the square root of 25.2 m/s squared plus minus 23.7 m per second squared, Which gives us the final velocity of the rock to be 34 .6 m/s. Next, for part, see we want to find the horizontal range from the base of the building to the point where the rock strikes the ground. Now we'll use the vertical motion, the Y component to find the time that the rock spends in the air. And we know that this time T. Is equal to the final speed V. Y minus the initial speed in the Y direction. Do not why? Over the acceleration A. Y. And this is minus 23 .7 m/s minus its initial speed. 16.3 m per second upward of uh minus G, which is 9.8 m/km2. This gives us your time Of 4.08 seconds. Now we can use this time to calculate the horizontal range so we can use another equation, X minus x not is equal to B, not X times T bless a half. Hey, X t squared. So this is the initial velocity in the X direction 25.2 m/s times a time of 4.08 seconds as the second term, which is zero. Since the acceleration in the X direction is zero, This gives us the range of the rock to be 100 and three meters. And lastly, we want to draw graphs for X versus T, Y versus T. V, X versus T, and V Y versus T, which look as follows. And here we have the graph of X versus t, why versus T. The X component of velocity VX versus T. And the Y component of velocity V y versus T.

So what is happening over here is there is a leaf of height. Age Ah, bodies thrown with velocity V and eat force like this. So this cause that we not And this is we finally are trying to find What is the manager of the velocity at the final location? So first of all, this is the problem in easiest down. If we call that a and B doorbell energy at a equals Total energy at B so half mv knock squared plus M g h Equus half and refinance square. So from here we find that the the final to be V Narc square. Thus G a do g eight squared off that we not is given Die seven square toe us two times 9.8 dives. The height off the leaf is 50 meter, so that would come out to be 32.7 meeting for a second

Garson told that Iraq is thrown with the velocity V zero at an angle Alfa zero from the horizontal of a building at a height of H, ignoring a resistance, calculate the speed of the rock just before it hits the ground and show that it's independent of Alfa Zero. Okay, so the rock is gonna move with projectile motion. We're gonna let why be in the upward direction? So therefore the acceleration from wise minus gravity minus g. So we're gonna combine equation 3.253 point 22 and 3.23 So what we have here, then is get the cursor selected. What we have is the squared is equal to be not squared. I have to co sign squared of the angle, say a zero plus V not times this sign of fate a zero minus gravity times time when all of that is squared. So let's go ahead and carry out that square. We find that this is equal to be not squared times the co sign squared of theta zero and you're also gonna have a V not squared sine squared data zero. So we'll just pull the V not term out front there and combine the science word and co sign spread zero terms since they haven't V not squared both associated with them. Of course, Sine squared plus co sign squared of any angle is equal to one. So that terms gonna end up being equal The one time to be not squared. This is minus two veena times gravity times, time, times a sign of fada zero plus gravity square times time squared. So then this is equal to be not squared minus to G multiplied by. So I just pulled to gie up front And this is gonna be V not times the sign of Fada Excuse me. Time to sign of Alfa zero Well supplied by time minus 1/2 gravity times Times Square. But you'll recognize what we have in the parentheses. There is simply the equation for the height, which we were told his h. So that means this is equal to V not squared minus two times gravity times the height H. So we just found the solution for the velocity. It's going to be equal to the square root of that. So the square root, because remember, this is a label of velocity. So the swear goes away. This is square routed then and that's our solution. Independent of Alfa Zero


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