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Problem 59

A balloon, rising vertically with a velocity of 16 feet per second, releases a sandbag at the instant it is 64 feet above the ground.

(a) How many seconds after its release will the bag strike the ground?

(b) At what velocity will the bag hit the ground?

Answer

$\begin{array}{l}{\text { (a) The bag will hit the ground after } 2.562 \text { seconds }} \\ {\text { (b) The bag will hit the ground with a speed of } 65.984 \mathrm{ft} / \mathrm{sec}}\end{array}$

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## Discussion

## Video Transcript

question 59 We are release at 16 feet per second. City Mission velocity, which is my ex prime at zero equals 16. And then I also know that of the reviews Sandbag hit 64 feet and we are assuming are a of T Acceleration equals negative, 32%. So are a of t A. He wants ask double crime. So those are things that we need to know and remember, we have a position function, the prime of the position. Punishing is our velocity, and our double crime is our acceleration. So now we go off and we try to find where three function. But we know our s double prime. So are its double crime equals negative 30 So defined as prime of tea. I take the integral of that. And that's gonna be well, negative. 32 tea. We'll see. What is Darcy? Long use zero and 15 for my right. Crying is 16 form negative, 32. But see, there horsey equals 16. So my s crime formula of Prime Minster equation equals negative 32 teeth plus 16. And now I integrate at that again to find my position function. So I have negative. 32 He squared, multiplied by the reciprocal of the exponents. Love 16 pain plus c So that becomes s a He won't negative 16 piece where but 16 p. See? And when I use zero in 64. So I have C bro equal. I'm sorry. 64 before e wombs. Negative. 16 times zero square plus 16 times zero. But see, they get CD will 64 c equals 64. So that makes the equation of my s equals negative. 16 piece. Where? A 16. T plus 64. Now I have all the information I need. The answer question for a M So are a They want to know what time. So in my regular position function, they wonder when it hits the ground. Some hero. His definitely whole negative 16 piece. Where? 16. T plus it's who are you and I saw proof. Uh, P what? Would you do this by either graphing queens? Where? Back during formula formula. But first, I'm going to factor out a negative 16 square minus D minus four. Therefore, a equals one b equals negative one and C equals negative core. So my quadratic formula negative b plus or minus the square root of B squared, minus bori all over two A. And when I put that in, I get Nate. I get one plus, Your Highness one minus four times, one times negative for over two times one. So I get one. Plus, you're minus the square root of 17 over too. Now, if I use the minus, I end up with a negative answer, Would you? No one can have negative time. So I'm just gonna do the one plus the square root 17 divided by two, which gives me approximately 2.6 seconds is the answer for part A and then for part B. They are asking us at what velocity? So I want to use my s prime p. So remember, that equation is negative. 32 tea plus 16. And I'm fucking in my quick night answer from heart A. So I needed a plug in the 2.6. Or I could plug in the one place where is 17 about Thank you was my exact on and six magnitude 32. What you depending on where you around it? Second. And that's your answer. Part

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