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A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is $ a(t) = 60t $, at which time the fuel is exhausted and it becomes a freely "falling" body. Fourteen seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to $ -18\;ft/s $ in 5 seconds. The rocket then "floats" to the ground at that rate.(a) Determine the position function $ s $ and the velocity function $ v $ (for all times $ t $). Sketch the graphs of $ s $ and $ v $.(b) At what time does the rocket reach its maximum height, and what is that height?(c) At what times does the rocket land?

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(a) $t \approx 45.5$ seconds(B) $$\begin{array}{l}{t=11.44 \sec } \\ {s(t)=1409.06 f t}\end{array}$$(c) $\mathrm{t}=45.6 \mathrm{s}$

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Derivatives

Differentiation

Volume

Campbell University

Idaho State University

Boston College

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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it's a travel knees. Another rocket is fired vertically, upward from rust as acceleration from the first three seconds is a tedious ekotto. Sixty taps T at which time to feel gets exhausted and it becomes a really falling body. Fourteen seconds later, darkies parachute opens. Andi, it's a downward with asked. It's lousy. Lay nearly two negative eighteen feet permit second in five seconds. Rocket, then lots to the ground at that ridge. But a determined the position function on the velocity function sketched the grafts off us on being the first one. He is between zero on DH three. We have Auntie, Is they caught you sixty times t and we have Wait, it's the culture. Thirty. I'm Steve Squire Andi. Us too. It's the culture, and Pam's is cube on. What he got you three. We have we three. It's the Culture two hundred on DH. Guarantee us three. It's also two hundred and seventy one. Key is between three on the seventeen. So we have Wait, it's the call to negative. I have to say something to it. This is connective. Three times he might just three us see costume number, see? And when key is they gotta three behalf with three years ago. Two, two hundred and seventy to see if they want you. Two hundred and seventy. And the jury if they caught you thirty two. So this is negative. Thirty two times He minus three us you handled. And seventy Castillo. Negative. Thirty two terms of a half. I'm steam minus three square. Last two hundred and seventy Time Steve minus three and plus See. And when he is there, go two three Behalf nasty. Is that got you? Two hundred and seventy. So here sea is also two hundred and seventy. This's equal to negative sixteen hams He might as three square Last hundred and seventy. Ramstein minus three. Last hundred and and Sandy. And when he is taken to you seventeen, we have we seventeen that this is Echo two negative one seven eight on DH. I'm seventeen. It's me Call too. Nine one war when he is between seventeen on dh two. We're half the last e Think for this from negative one, seven, eight two negative eighteen linearly. So we have Don't worry over that tea, this's equal to thirty two. So we have we is they come true thirty two hams, he minus seventeen minus y seven. Pit as Teo Sicko, too. Sixteen times T minus seventeen. Squire minus once, seven eight times, T minus seventeen plus some number. C so won t go to seventeen. This is nine one for say, is he called nine one floor on day one. He is He got you on you to have I. I wanted to. It's the culture or to war when he is greater than twenty two. Behalf, which he got to past the number Negative eighteen. And ask Tio, it's the culture negative. Eighteen Ham's T minus twenty two us. See, Since Monty's got twenty two as twenty two is you got a four to four. So that's pretty cool, too. Born to war thus and hell, the job Kid lands behalf of the last E with cheese. It's the culture. Thirty Times Square. Twenty is between serial kind three Conectiv, fifty two hams, T minus one, US two hundred and seventy when he is Caritas on Sound. Three On the last stand, seventeen thirty two times, minus seventeen, minus one seven eight And he is created creatures and seventeen. And the last time and the two This is detective fighting. When he is who returns on, I need to has to. It's the culture henhouse Tease Cube What He is between zero and three. Negative. Sixteen in minus three square, plus two hundred seventy pounds. T minus three plus two hundred and seventy. And he is greeted at three on the last seventeen sixteen times. T minus seventeen squire minus one seven night T minus Valentin Last nine one four when he is greatest and seventeen on the last time on the two negative eighteen ham's t minus twenty two US hold. True for when he is greater than twenty two. Now we can sketch there graph as follows. Before we were half, it's a graph is like just on DH for Graff is like this. This is a nasty This is a win. Had to be at which town? The rocket, which is the high school and what did the hat. So we have negative thirty two thousand eighteen minus three. US two hundred seventy is because a serial this is a week. So one way is equal to zero Their arcade ridges, the heist. So here he is. They called you eleven point three four three, seven five. Andi the distance was a hot is equal to negative sixteen minus three square US two hundred seventy humans. Three plus two hundred seventy Just plugging that this number to dysfunction. Behalf. US eleven point two three four three so far, but this is you. Go to one four zero nine point steer six feet. Hard to see what time the rocket. Alas, light as the cultural zero we have. This's negative eighteen times, T minus twenty two last warm, too, or we have he is about forty five point six.

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