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Aese roulQuiconTtty [eitonsdQue_don4cnc lefrec fall fun game system Is relcased from (rom Spoltx EneAnnag 1ppro nino cst height; Y of the frce fall: mil' the t...

Question

Aese roulQuiconTtty [eitonsdQue_don4cnc lefrec fall fun game system Is relcased from (rom Spoltx EneAnnag 1ppro nino cst height; Y of the frce fall: mil' the top of its reil and takes time t = 3.5 m1 [ehc acccleration dua (0 [0 reach the ground What is the gravity, g = 9.8 In/521 '4325 9 & 196m" 459,1

Aese roulQuicon Ttty [eitonsd Que_don4cnc le frec fall fun game system Is relcased from (rom Spoltx EneAnnag 1ppro nino cst height; Y of the frce fall: mil' the top of its reil and takes time t = 3.5 m1 [ehc acccleration dua (0 [0 reach the ground What is the gravity, g = 9.8 In/521 '4325 9 & 196m" 459,1



Answers

Use the following information. Scientists simulate a gravity-free environment called microgravity in free-fall situations. A similar microgravity environment can be felt on free-fall rides at amusement parks or when stepping off a high diving platform. The distance $d$ (in meters) that an object that is dropped falls in $t$ seconds can be modeled by the equation $d=\frac{1}{2} g\left(t^{2}\right),$ where $g$ is the acceleration due to gravity (9.8 meters per second per second). If you want to double the free-fall time, how much do you have to increase the height from which the object was dropped?

All right. So we're given velocity there, given the velocity and tracks off with the accent like component. So given velocity of something times I have something times J hats. So in the wind direction will only be concerned with, um, the J hat component on. So therefore we want we want to return to your equations of motion, Uh, which was chapter four. And so the displacement vertical displacement will be delta y and that is equal to V not what in the wide direction Times TV minus 1/2 g t squared, so v not in the wind direction. Times t is just this component in time teeth for this was 24 years per second times time, which is six seconds minus 1/2 times 9.8 meters per second. Squared for acceleration due to gravity times six seconds squared gives you vertical displacement of negative 32.4 meters. So then simply the change in gravitation potential. Angie is mg times this vertical displacement alto. Why? So that's one kilograms times 9.8 meters for second square. Times times what you just found here, minus 32.4 meters for vertical displacement giving us negative. 313.6. Jules for Delta. Why don't you

We have 100 number problem in which we have to formula D equal to one by two Duty a square, Another ridge ethical toe minus 16 ts square place as where Etch eyes, height, Any ideas? The distance as his initial height. And till the time. Okay. Okay. Yes. So as for the initial height, that is the in this case, that is the height on This is a model. Um that is the Hyatt. With respect to time Men's time the height faces increasing or decreasing with respecto time. And this formalizes ah, complete freefall formula. I am for complete freefall in this Ah, both can be the same when actual becoming called zero. So because when at zero the body has completely free fall to the ground. So zero call to minus 16 ts square plus s So this will be cool too as equal toe 16 square. And here as is in feet indeed in second. So both formula now are the same much value off G differs. Thank you

Okay, so we've got we solve this equation. Algebraic Lee and problem 51 now in problem 52 were just being told the check. That answer make sure works by graphing this equation 4.9 x squared minus 490. Which is kind of like taking this equation or this equation right here and just subtracting 490 from both sides of the 4.9 t squared minus 4 90 So we're just using why and said zero and T instead of Iraq's instead of tea. So here we go. Um, 4.9 X squared, minus 4 90 And we can barely see anything on a graph. But if I zoom out a little bit, you can see a couple of big, huge parabola here, and it's got roots. That negative 10 and positive 10 again. We can't have negative time, but we can have positive time. So it still makes sense to say that, um, you know that 10 seconds is the answer graphically

So as to, it took that apart of course, projected vertically upwards from the ground. So that takes the object the same amount of time it reaches maximum height as it takes with the dropped from that height back to the ground. Major height meters. Um uh I guess we didn't really need to measure height meters. Um because we never really needed to specify what G. Was. Uh So we have initial uh positions zero, initial velocity is rena and sometimes we cannot via zero. That's when it reaches peak. So what we're gonna do is figure out how long that is and then figure out the position that twice that we get back to zero so that it takes um uh just as long for it to fall as it did for to rise. Um So position given like this velocity is here, we can find T. One by setting the velocity equals zero. And that gives us T. One because we're not over G plugging that into here gives us um you know, x. Evaluating the T. One where we found that before was one half peanut squared over G. Now if we plug in two times tina so where is it after the twice the time it took to reach the top. Um And we see the men's I'll cancel out and you get zero. So it took T. One to rise up and took to um to t. One to rise up and fall. So it took T one time units to fall


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