5

Use the position function s(t) given by the following- s(t) Jim 0 _T-16p? 850 which gives the helght (in feet) an object that has fallen for seconds from height of ...

Question

Use the position function s(t) given by the following- s(t) Jim 0 _T-16p? 850 which gives the helght (in feet) an object that has fallen for seconds from height of 850 feet. The veloclty at timesecondsconstruction worker drops wrench from height of 850 feet; how fast will the wrench be falling after soconds- ftls

Use the position function s(t) given by the following- s(t) Jim 0 _T -16p? 850 which gives the helght (in feet) an object that has fallen for seconds from height of 850 feet. The veloclty at time seconds construction worker drops wrench from height of 850 feet; how fast will the wrench be falling after soconds- ftls



Answers

Use the position function $s(t)=-16 t^{2}+1000$, which gives the height (in feet) of an object that has fallen for $t$ seconds from a height of 1000 feet. The velocity at time $t=a$ seconds is given by $\lim _{t \rightarrow a} \frac{s(a)-s(t)}{a-t}$. If a construction worker drops a wrench from a height of 1000 feet, how fast will the wrench be falling after 5 seconds?

Hello. So here the object hits the ground means that we have to find the time taken by the object for the traveling distance of 1000 ft. Now at the time um the height of the object from the ground is well S. F. T. R. Function is equal to zero. So we have S. F. T. Which is equal to native 16 squared plus 1000 equal to zero. So um we can add 16 T. Square to both sides of this implies then that 16 T squared is equal to 1000 and dividing through by 16. Right gives us the T squared Is equal to 12,000 divided by 16. And taking the square root of both sides gives us that T. Is going to be equal to uh well 10 force Times the square root of 10. So this is the exact answer here. Um 10 4 times world of 10. That is going to be approximately equal to eight so approximately eight seconds. Um And then at the velocity at T. Is approximately equal to eight. We have um well we're taking the limit As as T approaches eight of 16 times T squared minus eight squared divided by eight minus T. Um And the 16 can come out front of the limit. So we have 16 times the limit as T approaches eight. Now this one factor the top here as T plus eight times t minus eight. Um All divided by eight minus T. So we can factor out the negative right, we get a negative 16 times the limit as T approaches eight of T plus eight. So that's just gonna be negative 16 times eight plus eight, which is going to be um negative 256 feet Per second. And the negative sign here indicates that the object is falling, so therefore um the impact velocity is going to be 256 ft/s. All right, take care.

You concussion. The position is given with respect to the time that you suggest to minus 16. 30 square last 500 velocity at any time the quest ways limit data have to a s a minus s t divided by a minus t like so we have to find the velocity at was 22 seconds. So we're to find limit theaters to do as to minus SD divided by two minus t. Right. So this is what we have to find. So we'll write the values off the function. That is. Yeah. Favor. Right. The values off the function T equals toe. We get minor self 34 36 minus minus 16. Describe plus 500 divided by two minus t. Right. When we further simplified, we get limit. They dashed to do 16 T square minus 64. Divided by minus one. If you take comedy minus two. Yeah, right. We can write the numerator as limit. They'd have to do 16 years. Commanders fall. We can like it s t minus two plus two, right. Divided by minus one. T minus two. So this time and this time will cancel out. So we will get minus off limit data has to do 16 T plus two. Now, with help off the egg substitution, we can find the velocity at equals. To do that is minus 16 two plus two, a close to minus 64. So minus 64 ft per second, A little bit of velocity after two seconds.

The given question. First of all, the first step is that we have to find the time taken to impact the ground. So I stayed. Sequels of the Polish in is given in Specter time. Minus 16 days squared plus 500 at the ground. Assets will be judo so we can find the value off T that is almost equal to 5.59 seconds. Right sort equals to five point. Finance against the venture will impact the ground. So whatever sort of from the election off velocity, we can find the velocity 20. A torch is 5.59 seconds s 5.59 My necessity. They read it by 5.59 minus days. We can write the values off the functions. That is Jeez. Oh, Minus minus 16 days, 12 plus 500 divided by 5.59 dynasty. When your father simplified, we get limit the tax too. 5.59 We can we can rewrite it as 40 minus under out 500 for the plus under 500. Yeah, right. They write it by if you take medicine. Common. The man is five point 59 now Okay, we can write it. US. Limit the attends to 5.59 40 plus 22.26 Okay. Yeah. If you take full common, we get T minus 5.5 night from this town. Like they rented by minus one day minus 5.59 This stuff will cancel out. So we will get the without off the X substitution, we get minus fall for multiplied by 5.59 plus 22.26 36 or 22.36 which is? It was two minus 1 78. Find a did feet per second. So this is the final solution minus 1 78.8. That fits per second.

Are they? The height of a falling object is given by hatred. T is equal to minus 16 t squared plus 60 40 plus 960. At what time does this hit the ground? The statement of the object hits the ground Is the statement Hate of T is equal to zero. This gives us the equation minus 16 T squared plus 64 t plus 960 is equal to zero. Everything here is divisible by 16. So get minus T squared plus 40 plus 60 is equal to zero. We're going to multiply out by minus one. So yet T squared minus 40 minus 60 is equal to zero. Ah, Now we need to find two numbers whose product is minus 60 and whose some is minus four because their product is negative number. We know that we're looking for a, uh, one number positive on one of the negative. So let's start by writing down thief actors off 60 of one and 62 on Day 33 Onda uh, 24 on board. 15. Five on 12 and six and 10 in fact, six minus 10 gives minus four and six times twice 10 is minus 60. So we have a factory. Ization is T plus six. T minus 10 is equal to zero. This toehold, we have a need T plus six secret 0 10 was T is equal to minus six or T minus 10 is equal to zero. Giving us t is equal to 10. The object wouldn't have fallen in the past so we need t to be positive. Giving us our final answer of t equals 10.


Similar Solved Questions

5 answers
Hendtt 14, Fruckm 47 Kentcla of ctarge +17,0UC and Xjia dl L09 * 10 *~Cqid ^ chero theteelectric field cf +626 N/C, What the displacement the particle atter conttanieasedDeroterioe Is5/-572
Hendtt 14, Fruckm 47 Kentcla of ctarge +17,0UC and Xjia dl L09 * 10 * ~Cqid ^ chero thete electric field cf +626 N/C, What the displacement the particle atter conttani eased Deroterioe Is5/-572...
5 answers
2.Graph the ! following points on the graph to the right draw the line, and then answer the questions: (10 _ pts) (-3,8) and (-3,4)What is the equation ofthe line?What is the slope of the line?What type of line is this?
2.Graph the ! following points on the graph to the right draw the line, and then answer the questions: (10 _ pts) (-3,8) and (-3,4) What is the equation ofthe line? What is the slope of the line? What type of line is this?...
5 answers
10. Use Part I of the Fundamental Theorem of Calculus to find the derivativ cos/ f() - of the function
10. Use Part I of the Fundamental Theorem of Calculus to find the derivativ cos/ f() - of the function...
5 answers
Huqnsuonsanb STYI Inoqe IOJOnnSUT a3ESS214" slduaue paluntun rajqtssod sluodMapaldQLJO} 46 u uopparp Jues 341 W J01234 uun 34} Pud799 + 58 22 = E J01224 34 W24ID
Huqns uonsanb STYI Inoqe IOJOnnSUT a3ESS214" slduaue paluntun rajqtssod sluod Mapald QLJO} 46 u uopparp Jues 341 W J01234 uun 34} Pud 799 + 58 22 = E J01224 34 W24ID...
5 answers
2. d_ =-9y dr 2 a) s(x) =&* b) y(x)=X' c} y(x) = sin(3x)
2. d_ =-9y dr 2 a) s(x) =&* b) y(x)=X' c} y(x) = sin(3x)...
5 answers
If the lines $frac{x-2}{1}=frac{y-3}{1}=frac{z-4}{-k}$ and $frac{x-1}{k}=frac{y-4}{2}$$=frac{z-5}{1}$ are coplanar, then $k$ can have [2013](A) exactly one value(B) exactly two values(C) exactly three values(D) any value
If the lines $frac{x-2}{1}=frac{y-3}{1}=frac{z-4}{-k}$ and $frac{x-1}{k}=frac{y-4}{2}$ $=frac{z-5}{1}$ are coplanar, then $k$ can have [2013] (A) exactly one value (B) exactly two values (C) exactly three values (D) any value...
4 answers
A30-UF capacitor is charged to an unknown potential initially Vo and then connected acrossan uncharged 10-HF capacitor: Ifthe. final potential difference across the 10-pF capacitor is 20 V,determine VoV29V6o @V13V20V27
A30-UF capacitor is charged to an unknown potential initially Vo and then connected acrossan uncharged 10-HF capacitor: Ifthe. final potential difference across the 10-pF capacitor is 20 V,determine Vo V29 V6o @ V13 V20 V27...
5 answers
Malc 69.0 mLol 0.22 M FONO,h-Sct up thc calculntion by sudcnt ncrds dlutc 4 042M PtNO, h solutlon to Tlicn cxlcululc Qulumc, millilatcr . of tlc plucing thc aluca with the colicct units Inio the cquation 042M FUNO;heolulion that ncededFmto Mantal
malc 69.0 mLol 0.22 M FONO,h-Sct up thc calculntion by sudcnt ncrds dlutc 4 042M PtNO, h solutlon to Tlicn cxlcululc Qulumc, millilatcr . of tlc plucing thc aluca with the colicct units Inio the cquation 042M FUNO;heolulion that nceded Fmto Mant al...
5 answers
V-'rzhHow many mitochondria can theoretically fit (at maximum) into a spherical eukaryotic cell with a diameter of 84 /m? Assume a mitochondrion has a shape of a cylinder with a height of 0.8 pm and a diameter of 0.6 um.372,000 margin of error #= 10%
V-'rzh How many mitochondria can theoretically fit (at maximum) into a spherical eukaryotic cell with a diameter of 84 /m? Assume a mitochondrion has a shape of a cylinder with a height of 0.8 pm and a diameter of 0.6 um. 372,000 margin of error #= 10%...
4 answers
4. (2 points) Here are the 13C NMR spectra for two of the compounds listed below: Draw the proper compound next to each spectrum: #C NMR2001501005012C NMR200150100~JLK
4. (2 points) Here are the 13C NMR spectra for two of the compounds listed below: Draw the proper compound next to each spectrum: #C NMR 200 150 100 50 12C NMR 200 150 100 ~JLK...
5 answers
Would it be possible to determine the acid neutralization powerof an antacid using titration without dissolving the tablet inacid? Explain.
Would it be possible to determine the acid neutralization power of an antacid using titration without dissolving the tablet in acid? Explain....
5 answers
Use the ratio indicate why:determinethe following seriesconvereentdivergent"3tictest fzils,245 #22()"2Z02;(2u) 2 (n)lEv
Use the ratio indicate why: determine the following series convereent divergent "3tic test fzils, 24 5 # 22()" 2 Z0 2; (2u) 2 (n)l Ev...
5 answers
Popular computer game at the price of $54 per unit; and at this price; A store has been selling players have been buying 70 units per month The owner of the store wishes to raise the price of the and estimates that for each $1 increase in price two fewer units will be sold each game month_ If each unit costs the store $25,at what price should the game be sold to maximize profit? 0 A 562B. S59Cs56D.$57
popular computer game at the price of $54 per unit; and at this price; A store has been selling players have been buying 70 units per month The owner of the store wishes to raise the price of the and estimates that for each $1 increase in price two fewer units will be sold each game month_ If each u...
5 answers
Solve the initial value problem by using the Laplace transform: y" + 4y = 8e +8(t - w/2) 26(t 7), y(0) = 1, Y(0) = 2.
Solve the initial value problem by using the Laplace transform: y" + 4y = 8e +8(t - w/2) 26(t 7), y(0) = 1, Y(0) = 2....
5 answers
[-73 Points]DETAILSLARLINALGB ROAo:MY NOTESPRACTICE ANOTHApply the Gram Schmldt orthonormalilzatlon process aiventransform the given basls for Rn Into an orthonorma basls Use the FucIldean Inne productand use the vectors the order which they are{(0, 0, 9), (0, 1, 1), (1, 1, 1)}
[-73 Points] DETAILS LARLINALGB ROAo: MY NOTES PRACTICE ANOTH Apply the Gram Schmldt orthonormalilzatlon process aiven transform the given basls for Rn Into an orthonorma basls Use the FucIldean Inne product and use the vectors the order which they are {(0, 0, 9), (0, 1, 1), (1, 1, 1)}...
4 answers
Find the domain of (g f(x) (Enter your answer using interval notation:) C,0OFind (f 0 O)(x)_Find the domain of (f O(x) . (Enter your answer using interval notation ) ~CO,Oo )Findg)(*) =Sx +16Find the domain of9)(*) (Enter Your answei using interval notation_16Need Help?Subinit Answrer
Find the domain of (g f(x) (Enter your answer using interval notation:) C,0O Find (f 0 O)(x)_ Find the domain of (f O(x) . (Enter your answer using interval notation ) ~CO,Oo ) Find g)(*) = Sx +16 Find the domain of 9)(*) (Enter Your answei using interval notation_ 16 Need Help? Subinit Answrer...

-- 0.020230--