a-ball-is-thrown-vertically-upward-with-an-initial-velocity-of-80-feet-per-second-the-distance-s-in-

Name: a ball is thrown vertically upward with an initial velocity of 80 feet per second the distance s in
Uploaded: 2020-07-21
Duration: 3 min 25 s
Channel: Numerade
Description: A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance $s$ (in feet) of the ball from the ground after $t$ seconds is $s(t)=80 t-16 t^{2}$

Question

A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance $s$ (in feet) of the ball from the ground after $t$ seconds is $s(t)=80 t-16 t^{2}$

Ethan Dotson-Kelly · Accepted Answer

this problem is a question about a ball that has been thrown into the air and is being affected by gravity and bringing it back to the earth. This equation is representing that ball being thrown in. The air is been thrown at 80 feet per second and this is acceleration due to gravity being brought back down of negative 16. And so what this question is asking us is two parts part a is asking us win. When is a time question? When will the ball land back on the ground? And that will happen when the Prabal Owen s of t will equal zero when the graph equals zero. And we want to know when this occurs. Well, it equals zero when the time when the y value is zero. That&#x27;s what this is telling me when the Y value is equal to zero. What is the time so we can use a graphing utility to help us out. So here I have the equation. S f T equals 80 T minus 16 T square. And here&#x27;s the problem. Here is where it starts at 00 It&#x27;s thrown into the air and it reaches a peak at 2.5 seconds of 100 feet and gradually falls back to the ground and it crosses. The X axis had five. So here is when it lands on the ground. So how long did it take to land back on the ground? Five seconds. So the answer to a is X equals five. And let&#x27;s just go ahead, make it correct. Five seconds. Question be asks us the question For what time? How long is the graph above? For what time? Tea is the ball more than 96 feet above the ground. For what time? How long, Basically, is it above 96 feet? So what that means is we&#x27;re asking Win His sf t Part B is asking Windows S of t greater than 96. That&#x27;s what the question is asking us. And so again we can use the graphing utility to help us out. So here I have the line of y equals 96 feet and it&#x27;s a vertical line horizontal line, and I want to know how long. What time interval is it above? It&#x27;s above 96 feet between two and three seconds. So that&#x27;s exactly what I&#x27;m going to say between two and three seconds to is less than X, which is less than three, which means between to and three seconds.

Ankit Gupta · Answer

in this question. Ah, ball is thrown vertically upwards with the initial velocity off 80 feet per second. The distance as off the ball from the ground is given as after t seconds as off T equals 80 miners. 16 p square. No, in the first part off the question, it is us to find out that after how much time the Baldwin strike the ground. So initially we know the distance is zero. The time is also zero. Now, excavating as as equal to zero we will get zero week was 80 minus 16 T square. Solving it, we can light it as a TT miners 16 T square equals zero. We can take 16. Take woman on we get five minus t inside the bracket. Now solving it, we get to answers. Peak was zero or T equals Fife. No, big was zero is the initial time only. So the Baldwin strike the ground after five seconds. So the answer is D equals five seconds. Now in the people, we have to calculate the time for which the ball is about 96 feet. That means the distances greater than 96. Or we can say as softy is greater than 96 as off PS given is 80 T minus 16 t square greater than 96? No, we console this inequality toe. Get the answer. For the time the inequality can be really done as a TT minus 16 D squared, minus 96 greater than zero. Also, we can rearrange them and write them as minus 16 t squared plus a T T minus 96 greater than zero multi playing with a minus sign on both the sides. We get 16 t square minus 80 plus 96 less than zero whenever we multiply with a negative sign on both sides off the inequality. The sign off the inequality changes Now solving this, we get to factors. First of all, we will divide the inequality. With 16 we get T square minus 5 50 plus six less than zero now forming all the factors we get two factors T minus two and B minus three less then Zito the product off. These two should be less than zero. Let us see this happens between which values. So we will take different cases now checking for different values off t we know T minus two If people tell you less than two in T minus two, it will be negative. Now at equal Toto, it will be zero between 2 to 3. We put any value in T minus two. It will be positive at equals three. It will be positive on if you put greater than three then also it will be positive now, 40 minus three. When the value off, these less than two, we&#x27;re going to get a negative answer. 40 minus three now at equal stools. So we will get a negative answer. If you put any value between 2 to 3, we&#x27;re going to get negative Answer on. If at Peak was three, we will get zero. And if the value is de greater than three, we&#x27;re going to get a positive answer now, looking for the results, we can just I conclude that minus and minus, we know the answer will be. Plus, here it will be zero. Here it will be miners. Here it will be zero. And here it will. Plus Now we help you look for less than zero. That means in negative and this is the option. That means the correct answer will be that the lies between go to three during this interval, but have in two seconds to three seconds the ball will be about 96 feet.

John Irizar · Answer

for our position were given the function s equals 80 T minus 16 t squared. Now, to find the maximum height that the bone reaches, that would be where our velocity is. Zero. In other words, it&#x27;s stops going upwards and starts coming back down. Now our velocity is the derivative of the position which would give us a T minus 32 t setting this equal to zero. We get negative 32 t is equal to negative 80 and T is equal to 2.5. So that gives us the time when the ball reaches its maximum height, not the maximum height. For that, we will have to take our 2.5 and put it back into our position function. Eso the position at time to 0.5 would be 80 times a 2.5 minus 16 times 2.5 squared. And evaluating this we get 100 feet is the maximum height that the ball reaches. No, I&#x27;m going to draw very roughly here the shape of our position and we know want to know. We know that this here is 100 fee. We want to know the velocity of the ball on its way up when it passes 96 feet and also on its way down. So let&#x27;s find out what time it reaches 96 feet. So I will take our position function 80 T minus 16 p squared and said it equal to 96 to find the time that it reaches that point. So I&#x27;ll bring everything over to the right hand side. I&#x27;ll have 16 t squared, minus 80 t plus 96. Now everything here is divisible by 16. So let&#x27;s go ahead and get rid of that factor. Well, t squared minus five t plus six. And this factors into T minus two and T minus three. So the two points occur and two seconds which would be on its way up and then at three seconds on its way down. Now let&#x27;s find our velocity at those two points. So the velocity at T equals two. I would give us K G minus 32 times two, which will give us 16 feet her second. The velocity AT T equals three would give us a D minus 32 times three, and this gives us negative 16 feed her second the negative, indicating that it&#x27;s coming back down

Tiffany Tran · Answer

the ball hits the ground when the heights is zero. So you do. Zero is equal to negative. 16 square T square plus 80 T plus 96 thing gonna factor out negative 16. So we&#x27;re left with cheese squared minus five T minus six and can simplify this even more. So we&#x27;ll have negative 16 t plus one and thine minus six. And then you&#x27;re gonna set each one equal to zero, so t plus one equals zero will be negative one and then t money six equal to zero B after six seconds. So the recent y T is able to make it one. Doesn&#x27;t it exist? It doesn&#x27;t make sense because you could not.

Ankit Gupta · Answer

First, we have to find the time taken by the ball. Two strikes the ground for this. We have given that the distance as his equal toe 96 plus eight e minor. 16 a square we take as is equal to zero. That means the distance is equal to zero when the ball hits the ground. So 96 plus 80 80 minus 16 e square is equal to zero, which implies that minus 16 80 square plus it e last 96 is equal to zero x 16 Coleman. From this equation, we get minus T Square. Last five e plus six is equal to zero. When we make factors off this equation, we get minus d plus six e plus one is equal to zero. We get to values off the, which are t is equal to minus one earned. Six. We neglect negative value, so T is equal to six second. So the time taken by the ball two strikes. The ground is six seconds. Now we have to find when the ball past the top of a building on its feet down. For this, we have given that distance, as is equal to 96 feet. So we have Equation 96 plus a T T minus 16. E square is equal to 96 which implies that minor 16 e square last eight e t is equal to 96 minus 96 taking 16 Comin from here, we get minus T square. Last five is equal to zero. Then we take Bea. Comin from here minus e e minus five is equal to zero. There are two values off key which are is equal to zero and five. We neglect zero so is equal to five seconds, which means that the time taken by the ball past the top off the building on its way down is five seconds, which is a very quiet answer.

Heather Zimmers · Answer

All right, So we&#x27;re given the equation for the height ever projectile, and we want to start by finding the velocity after two seconds and four seconds. And so we&#x27;re going to find the velocity in General V of tea by finding the derivative of the height function. So the derivative would be 24.5 minus 9.8 t Now, to find the velocity it to weaken substitute to in there. So we have 24.5 minus 9.8 times two, and that gives us 4.9 and the units would be meters per second and the velocity at time four will just substitute a four in there and we get negative 14.7 meters per second for part B. We want to find the time when the projectile reaches its maximum height and we have two ways to do this. One way is sort of an algebra two way. We recognize that this is a parabola and it opens down and we could find the Vertex and the X coordinate of the Vertex would be the time. The other way is a calculus way. And we would realize that the velocity would be zero at the time when it&#x27;s at its maximum point, because we would have a horizontal tangent line there. And so I say we do the calculus way since we&#x27;re in calculus. So we want the velocity equals zero. So we take our velocity 24.5 minus 9.80 and said it equal to zero. And we saw for teeth. So we have 9.8 t equals 24.5 and we end up with t equals 2.5 seconds. So that is the time when the projectile is at the maximum height for part C. We&#x27;re finding the maximum height. So we&#x27;re going to take the time we just found, which was 2.5 seconds and substituted into our height equation and will compute this and we end up with 32.6 to 5 meters for part D. We want to find the time when it hits the ground. So when it hits the ground, its height is zero. So we&#x27;re going back to the height equation on. We&#x27;re setting it equal to zero. I&#x27;m going to rearrange the terms of little bits. We have negative 4.9 t squared plus 24.5 t plus two equals zero. Now, unfortunately, this is not factory ble. So we&#x27;re going to solve this equation with the quadratic formula, and I&#x27;m going to start by multiplying the whole equation by negative one just so that we can lead with a positive coefficient. Just seems to make life a little bit easier. Now, we&#x27;re going to use the quadratic formula so we have t equals the opposite of B over two, a plus or minus the square root of B squared minus four a. C all over two a. And you&#x27;re gonna simplify that and work that out and we end up with 2.5 plus or minus the square root of 6 39.45 over 9.8 and you&#x27;re gonna put that in your calculator and you get to answers approximately 5.8 or negative 0.8 But you realize that you&#x27;re not going to keep the negative time in this context. So just the positive one now, because for party, we&#x27;re going to use this number for something else. We might store that in our calculators, so that we will be more accurate for part e for party were finding the velocity when it hits the ground and we use our velocity equation and we substitute that number we just got in the previous part the approximate values 5.0, wait. It would be a good idea to use the stored value so you don&#x27;t lose too much accuracy. So we have 24.5, minus 9.8 times five point a 5.0.8 and we end up with approximately negative 25.3 meters per second.

Problem

A ball is thrown vertically upward with an initia…

Problem 33 Hard Difficulty

A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance $s$ (in feet) of the ball from the ground after $t$ seconds is $s(t)=80 t-16 t^{2}$

Answer

a.5 seconds
b. between 2 and 3 seconds

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a.5 secondsb. between 2 and 3 seconds

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Anna Marie V.

Caleb E.

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Michael J.

a.5 seconds
b. between 2 and 3 seconds

Michael Sullivan

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