if-a-ball-is-thrown-into-the-air-with-a-velocity-of-40-mathrmft-mathrms-its-height-in-feet-after-t-s

Name: if a ball is thrown into the air with a velocity of 40 mathrmft mathrms its height in feet after t s
Uploaded: 2020-04-01
Duration: 3 min 24 s
Channel: Numerade
Description: If a ball is thrown into the air with a velocity of 40 $\mathrm{ft} / \mathrm{s}$ , its height (in feet) after $t$ seconds is given by $y=40 t-16 t^{2}$ . Find the velocity when $t=2$ .

Question

If a ball is thrown into the air with a velocity of 40 $\mathrm{ft} / \mathrm{s}$ , its height (in feet) after $t$ seconds is given by $y=40 t-16 t^{2}$ . Find the velocity when $t=2$ .

Bobby Barnes · Accepted Answer

we&#x27;re told a ball is thrown in the air with velocity afford a few per second, and its height can be given by the equation. Why is even 40 team minus 16 t squared? You want to find a velocity when time is acquitted, too. Now the thing will need to recall from physics is that velocity is equal to the derivative or the rate of change of our displacement. So we normally right, this is like Delta lie or don&#x27;t t. But in this case, what we&#x27;re really finding is the derivative of this function active. So if we were to call this function, f a t were wanting to find what is f prime of two. So what we would do for that is the limit as tr purchased two o f t minus Uh uh too All over. T minus two. Now we need to figure out wood after two is so let&#x27;s see. Effort to is going to be so it B a D minus 16 times two squared, which is or which is going to be 64 and then subtracting those should give us 16. So we&#x27;re gonna plug 16 in perfect too. So we&#x27;re gonna have the limit as t approaches to of so effort ease the puncture were given, and I&#x27;m just going to rewrite it like this. Where e. T squared is first. That may have minus 16 all over tea and minus two. Now, if we were to just plug this in directly, we would get 0/0, and I don&#x27;t know what that means. So what we can try to do is defied these two functions to see if they cancel. And I&#x27;m going to do this with synthetic division off on the side here. So it&#x27;d be too on the outside because that&#x27;s the root of T minus two. Read a negative 16 40 negative 16. So dropping the 16 down to that give us negative 32 which would give eight and then two times eight is 16 0 So that means this would be negative 16 x plus, not expert t t plus eight. Which means we can rewrite this us the limit as t approaches to, uh, negative 16 t plus eight. And now we can go ahead and plug to win directly into this, which would give us so negative 16 times two special. Let me just go ahead and write it out first. That&#x27;s gonna be negative. 32 plus eight or negative. 24. And the units with this would be feet per second. So this would be our velocity after two seconds.

Anthony Han · Answer

So here we give an example of a certain function where we have Y equals 40 t minus 16 t squared. And were given information that this is our position function, And the derivative of the position function gets the velocity function, which is 40 -32 t. So this is our velocity function And were asked to evaluate the velocity at time of T equals two seconds. So why prime of two would be equivalent to 40 64? So this would be equivalent to negative 24? And our units is specifically in this case feet per second, and this basically shows that one and the ball is thrown into the air at time T equals two seconds. This is giving the part of basically the falling face of the ball, so it&#x27;s after the ball has already reached its peak, and this is our final answer.

Wesley Hines · Answer

so we know that the average velocity for any given time period is going to be equal to Displacement X over the displacement of teeth. So to solve this problem for the four different time periods, we&#x27;ll have to come up with the distances, threat and the different times there. So do this. We&#x27;re just gonna make a little tape, so you will have the displacement of tea, each one we&#x27;ll have what time that gives us looking. Then we will get the value of why our X It&#x27;s gonna be why, in this case, because, um, we&#x27;re working with a ball that is in the air. So displacement of X is going to be represented is why in this problem, and we have the displacement of oy and then finally, we can use all of those to give us the velocity at a given point. So the first item had 0.5 seconds. Displacement of T is going to be 0.5. Sense of the time. A team 0.5 seconds is going to be two points. The next item, at 0.1 seconds will be 0.1. Give us two points. One. The third item is 0.5 seconds and this would give us to buy. And then finally, plane 01 seconds. This will give us 2.1. And now we just plug in these four values of T into why? To get the distance. At that time, This will give us zero 13.44 14.76 and 15.7 six. Not a Kightly. The displacement. Why? We&#x27;re just going Teoh, plug all of these values, Um, we&#x27;re gonna subtract 16 from And the reason we&#x27;re subtracting 16 from them is because from why is at equal to tease you would have to, um why equals 16 cause we&#x27;re trying to find the displacement from AT T equals two vs at these four different time points. So we&#x27;re gonna take the times we just came up with why and subtracting from 16. This would give us negative 16 negative 2.56 and negative 1.24 and the negative 0.24 So now, since we know that the is you go to the displacement of X over the displacement of two, we can just plug in our values for the displacement to you in our values. For the displacement of why to solve for T. And this would give us negative. 32 negative, 25.6, negative 24.8 and negative 24.16 And these represents the average velocities or the ball thrown in the air at 0.5 point 105 and 0.1 seconds after t equals two. Now to find the instantaneous philosophy, Um, we could do this graphically. So we notice here that 2.5, it&#x27;s negative. 32 2.1 negative. 25 16 and so on. And we could knows that the closer and closer week que zero seconds, Uh, because instantaneous velocity will be you can view it as if we were to plug in 2.1 So many. It&#x27;s so close to two that its prey, um school knows that as we get closer and closer to two with our time, the velocity keeps decreasing and decreasing it closer to negative 24. And that is actually enough. Um, enough now is this for us to say that the instantaneous velocity as time, bro, just two seconds is negative 24 in this case, feet per second. So you know that the average velocity after two seconds, given those four time points, is this column here and we know that the instantaneous philosophy his native 24 feet percent

Daniel Nolan · Answer

So in this question, a ball is being Donald puts on its height in feet after. See seconds is given by this equation. Why? Because 40 t minus 16 t squared, and it&#x27;s asking us to find the maximum height attained by the ball. So why is the max is the height of the ball after tea Seconds to find the maximum height, we just need to find the maximum value of this equation, and then they&#x27;ll give us the answer. So to find the maximum value, I&#x27;m just going to use on a equation for the I&#x27;m to find the that the tea co ordinate for the Vertex on. Then I&#x27;m gonna send that back into the equation. Allow give, Millie. Now, give me my maximum value in feet. Okay, So hit. I&#x27;m gonna use this equation. It&#x27;s gonna be minus b over to a and I&#x27;ll give up me on the team. Coordinate off the vertex. So minus B here is minus 40 on dhe to a is minus 32. Okay, just gonna simplify that with my calculator. And that gives five over four. So if I sold five over four back into the equation now, I&#x27;ll get the maximum height attained by the balls of your feet. That&#x27;s gonna be 40. Type by five over four, minus 16. Touched my five over for all squared. Looking right into my calculator. I get it 25 that&#x27;s in feet. And that is the maximum height attained by the bar. Okay, thank you very much for listening. If you have any questions about that, you can email me at Daniel D. J. P. H. Not known, uh, at gmail dot com. There we go. Thank you very much. Listening and wish you the best of the best for your studies.

Amrita Bhasin · Answer

this question instructs us to find the maximum height obtained by the ball. What we know is that we have the function after of tea is 40 T minus 16 T square. This function has a maximum value because R is negative. Therefore, we can use the formula negative be over to eight solved. We know our B is 40 or a is negative. 16. This gives r T as five divided by four plug after five divided by four n Again, This is into the original function we&#x27;re solving for our second co ordinate tweet. We end up with 25 because this is a word problem. Don&#x27;t forget your unit. 25 feet is the

Aamir Mithaiwala · Answer

all upward and we want to know at what time is a below a certain certain. So we want to know where this ball is below 100 feet if we threw it at 200 feet. And so now we are given a a height function. But we want to know where that height is less than 100. And so if we have the quadratic or we have the function of the height, we want to know where it&#x27;s less than 100. We can figure out where where we can. We can manipulate that and say OK, so we have we have negative 16 t squared negative 16. You have 16 t squared plus 40 t and then since we subtracted 100 to get it to make make the height lessons here is that we have plus ah, 100 is less than zero feet. And so now we can solve using the quadratic formula. So we have negative 40 plus or minus plus or minus the square root of B squared, which is 16. It ISS 16 100 minus for times negative. 16 4 times negative 16 times 100. So that&#x27;s plus 6400 plus 60 or 100 Ah, 6400 over two times Negative 16. Negative, 30 to. And so if we were to solve for this, we would get we would get the root of the square root of 1600 plus 6400 is the same thing as saying is the same thing of single the square of 8000. So the square root of 8000 is 89.442 But if we say negative for you, plus this value. So if we were to softens, we can we can figure out the values of T. It&#x27;s a let&#x27;s a T is equal to well, we have negative 40 plus 89.442 which is a square of 8000 that and then provided by negative 32. That leaves us with negative 1.5 negative 1.5 and the other instance in which case we subtract negative 40 minus that value negative. 40 minus the square root of 8000 we&#x27;re left with. We&#x27;re left with 4.4 so four point zero for Or let&#x27;s keep it at four points here or four seconds, so it&#x27;s round to the nearest whole number or point. But let&#x27;s round two, the newer stencil. So we have We have two instances. We have a negative time and we have a positive time. So we already know that in real world applications, negative time doesn&#x27;t really we don&#x27;t worry about that. So, missus is we have t is equal to four. And so if we were to draw a graph of this, we have at at time T equals zero Time T equals zero were at some value 200 and we go down. And so we want to know we want to know Where is this? Where is this? Less than some value. And so if that occurs at four seconds, T equals four seconds. We know that when t that when t is greater than for that is when our height will be less than 100 feet

Problem

If a rock is thrown upward on the planet Mars wit…

Problem 27 Easy Difficulty

If a ball is thrown into the air with a velocity of 40 $\mathrm{ft} / \mathrm{s}$ , its height (in feet) after $t$ seconds is given by $y=40 t-16 t^{2}$ . Find the velocity when $t=2$ .

Answer

$\left.v\right|_{t=2}=-24 \mathrm{ft} / \mathrm{s}$

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$\left.v\right|_{t=2}=-24 \mathrm{ft} / \mathrm{s}$

Biocalculus Calculus for the Life Sciences

Grace H.

Kayleah T.

Caleb E.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

James StewartBiocalculus Calculus for the Life Sciences

Grace H.

Kayleah T.

Caleb E.

Michael J.

James Stewart

Biocalculus Calculus for the Life Sciences