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A doctor, preparing to give a patient an injection, squirts a small amount of liquid straight upward from a syringe. If the liquid emerges with a speed of $1.5 \mathrm{m} / \mathrm{s},$ (a) how much time does it take for it to return to the level of the syringe? (b) What is themaximum height of the liquid above the syringe?

(a) 0.31 $\mathrm{s}$(b) 0.115 $\mathrm{m}$

Physics 101 Mechanics

Chapter 2

One-Dimensional Kinematics

Motion Along a Straight Line

Hope College

University of Sheffield

McMaster University

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Okay, so in this problem, we are squirting a small amount of liquid. It's straight upwards from a syringe. I cannot draw a syringe. It's that's from the standard problem. First, we know that this liquid reaches a maximum height, then begins to fall again until he reaches the same height off this strange. Okay, so let's see your problem. It's the problem, say's that the initial speed off the liquid was 1.5 meters per second. We know that just the liquid is under the gravity. The separation off nine points. You're one meters per second square. And the first question is, how much time does it take for the liquid returned to the level? Simply how much time this hope process took? We know that the time to the liquid go up is equal to the time to the liquid to go down. So we free discover their time to the secret go up. We just need to multiply by two. And we have d'oh whole time of the process. So let's think. Let's look on Lee. So the first part off this movement and the first part of the movement we know we have, uh, initial velocity off 1.5 meters per second. We have a gravity, the separation negative because the gravity's points in the opposite direction. Off the movement, off nine points. You are meters per second square and we want to discover death time. So simply years velocity as a function off time putting minus g here because we know we have to use minus G. Well, that's put a positive sign and change later. So you guys get not confuse. It's always positive, but the value off the gravity for this problem is going to be minus. Okay, so let's see. Final velocity zero because he reaches his maximum height. Initial velocity 1.5 miners, nine point 81. So the time to go up it's going to be 1.5 divided by 9.81. And this and this is equals two year of point 15 seconds. So the entire time off the movement we need to answer. It's just multiply this by two. I'm going to be zero point tree seconds. This is the answer for the first item. This second item I can be what we want to discover. We want to discover the maximum height. That means the maximum height off the liquid. Okay, so we already know the time. You already know velocity can choose. Any equation to calculate is I'm going to choose the velocity as a function off position because I think is the easier one. But you can also use a position as a function of time and you get the same result. So let's see. Final velocity zero initial velocity, 1.5 square minus two times 9.81 doubt x so that maximum height. It's just going to be two points. 25 divided by two times 9.81. This is going to be equal 20.11. Yes, that's right. Zero point 11 5 meters. This is the maximum height off the liquid after after leaving this revenge. So this is the final round

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