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Two arrows are shot vertically upward. The second arrow is shot after the first one, but while the first is still on its way up. The initial speeds are such that both arrows reach their maximum heights at thesame instant, although these heights are different. Suppose that the initial speed of the first arrow is 25.0 $\mathrm{m} / \mathrm{s}$ sand the second arrow is fired 1.20 $\mathrm{s}$ after the first. Determine the initial speed of the second arrow.

$v_{20}=13.24 \mathrm{m} \cdot \mathrm{s}^{-1}$

Physics 101 Mechanics

Chapter 2

Kinematics in One Dimension

Motion Along a Straight Line

Neil D.

June 2, 2021

From his bedroom window, a boy drops a water-filled balloon to the ground, 6 m below. If the balloon is released from rest, how long is it in the air

Cornell University

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okay. In this problem, I have two arrows. Aargh! One end a row two Um, now we know that era one is initially shot with a velocity of 25 meters per second and we also know that we're on the planet Earth. So the acceleration due to gravity of arrow one is negative 9.8 meters per second squared. His problem talks about the fact that these two arrows reach their maximum height at the same time. And what that means for both our arrows is their final velocity zero meters per second at that maximum height value. Okay, so at some time after being launched, this arrow reaches zero meters per second. Um, now, the second error was not launched at the same time it was launched 1.2 seconds after. But that means is the time the second era was in the air is not t rather, it is t minus 1.2 seconds. So we don't know exactly what it is, but we do know how it's related to the time. In part ones, we can define both of those variables using only one letter T um, and Arrow two's also on the planet Earth. So we have an acceleration of negative 9.8 meters per second squared. Okay, So our end goal here is to be able to figure out what that initial velocity of a road to was, Um, And looking at this for kin O Matics, remember that any time you have three numbers, you know you can solve for the other two. So right now I have three numbers that I know about era one, but not three numbers that I know about a row two. So I'm going to use the variables I know in for era one to find the time that era one is in the air. Plug that into equation to and use that to find the initial velocity of that arrow. So with that, let's look at what we have. Um, for the first part, we don't know the distance, and we also don't care about it. So what? I'm looking at my equations. I'm going to use the 1st 1 because it doesn't have an accident. It is just V equals V not plus 80. So when I plug in my numbers here for part one, we have zero equals 25 minus 9.8 t. So 9.8 e equals 25. And the time that arrows in the sky is 2.55 seconds. Okay, um, I'm gonna move this work out of the way a little bit because that gives us our third piece of information that we need, um, to determine what the initial speed of aero to waas. Because since our total time is 2.55 and we know the time Ferrero to is 1.2 less than that, our time for Aero two is 1.35 seconds. And now we just need to find this initial velocity. So using the same equation, we have final equals. Initial plus acceleration multiplied by time. Then if we rearrange it, our initials would be equal to our final minus acceleration, times time. And we get our initial velocity. Once we plugged these things in of 13.23 meters per second. That's how fast that second arrow was shot

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