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Referring to Example $2-21$ Suppose the balloon is descending with a constant speed of 4.2 $\mathrm{m} / \mathrm{s}$ when the bag of sand comes loose ata height of 35 $\mathrm{m}$ . (a) What is the amount of time the bag is in theair? (b) What is the speed of the bag when it is 15 $\mathrm{m}$ above theground?

(a) 2.27 $\mathrm{s}$(b) 20.24 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 2

One-Dimensional Kinematics

Motion Along a Straight Line

Alayah M.

February 2, 2021

What is the speed of the bag when it is 17 m above the ground?

Cornell University

Hope College

University of Winnipeg

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Okay. So in this problem, we have a balloon. Ah, the sending in the air. If constant speed off 4.2 meters 1st 2nd Ah, then a bag of sin. Detach from the from the balloon from a height off. Let's see our 35 meters. So the problem wants us to find out what was the time? That the biggest sin. You stay in the air on two hits the ground, so we need to find out the time. Well, since the only equations is the only information we have is the position of the bigger sin. We're going to use the formula off the position as a function over time. So what is the initial velocity of the bag Gerson sees? The biggest sin was attached to the balloon and about almost sending with the velocity off 4.2. So the initial velocity of the biggest send also is 4.2 meters per second. So here we have 35. You cruise 4.2 t was nine point 81 divided by two T square. We're going to move, supply all the expression for two. So we're going to have 17 8.4 d'oh was nine point 81 t square. Okay, so this is our contracting expression, and we know how to Silver car Direct equation. So let's come here. We're going. We're going to rearrange the terms, so we're going to have nine points. Anyone? Do you square waas eight point for Keep my noose 70. This is Echo Zero. So since we know the solution for D protracted creation, it's going to be t e grows miners 8.4 plus minus day square roots off 8.4 square minus four times miners 70 times nine point 81 All of this in the square roots and all of this divided by two times nine point 81. So simply find this. We have 8.4 waas minus they square route off at sea two point 2000 in 817 point 36 divided by on that C divided by two times 9.81 is just 19 point 62. Okay, so the solution for this we have two solutions a positive solution in a negative solution. Since time cannot be negative, we're going to choose the positive solution. So the answer for the first item. It's going to be t if course is just to 0.27 seconds. This is the answer to the first item and the second item of the problem. We want to find out the speed of the bag of sin when he is a 50 meters above ground. So let's see this second ison. We want to find out the speech. Final speed the beggar send when he's in the position. 25. Why is the position 25 actually Position 20. Why is the position 20? Because the entire entire position is 35 and we want to know. Let's try to draw this. We have a height in here off 35. We want the velocity of the bag of sand when he is a 15 meters above the ground. So since our zero is in the balloon, the position we're going to calculate is when there is 20. So let's see, we're going to years the equation for velocity, because it's what we want to discover. He's zero plus GT should be a team in here, so v it's going to be the zero that is 4.2 was nine point 81 times t We don't have the time so apparently disagree. Shin. It's not possible to solve. So we're going to try order equation that involved the velocity. We're going to use the velocity as a function of position because we don't have the time of 50 meters. But we have the position so we can use this instead. The square Easier square. Well, us too. You doubt? X So we're going to have four points. 4.2, 4.2 square plus two times nine point Anyone times 20 Have a scratch. You so ve scratched. It's going to be it's going to be 400 20. Oh, sorry in 10 point zero for So the square roots of the velocity. It's going to be 20 point 24 meters a second and this is the final answer for the second item and the final answer to the question

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