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(III) A rock is thrown vertically upward with a speed of12.0 $\mathrm{m} / \mathrm{s} .$ Exactly 1.00 $\mathrm{s}$ later, a ball is thrown up vertically along the same path with a speed of 18.0 $\mathrm{m} / \mathrm{s}$ . (a) At whattime will they strike each other? (b) At what height will the collision occur? (c) Answer $(a)$ and $(b)$ assuming that the order is reversed: the ball is thrown 1.00 s before the rock.

a) 1.45 sb) 7.10 mc) they do not collide

Physics 101 Mechanics

Chapter 2

Describing Motion: Kinematics in One Dimension

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

University of Michigan - Ann Arbor

Simon Fraser University

University of Sheffield

Lectures

03:28

Newton's Laws of Motion are three physical laws that, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows: In his 1687 "Philosophiæ Naturalis Principia Mathematica" ("Mathematical Principles of Natural Philosophy"), Isaac Newton set out three laws of motion. The first law defines the force F, the second law defines the mass m, and the third law defines the acceleration a. The first law states that if the net force acting upon a body is zero, its velocity will not change; the second law states that the acceleration of a body is proportional to the net force acting upon it, and the third law states that for every action there is an equal and opposite reaction.

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

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(III) A rock is thrown ver…

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(II) A stone is thrown ver…

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From the top of a tower of…

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A ball is thrown upward fr…

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A ball A is dropped from a…

03:53

(III) A ball is dropped fr…

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A rock $(m=2 \mathrm{kg})$…

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A stone is thrown vertical…

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08:29

A $0.100-\mathrm{kg}$ ball…

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A small rock is thrown ver…

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this problem. We have a rock and a ball and the rock is thrown upward at 12 meters per second and the ball is thrown upward in 18 minutes per second. Okay? And I'm trying to find when they collide and they're gonna collide when their heights of the same. And so if I say that Delta y for the rock is B zero for the rock times tea, I'll just say t one because our times are gonna be different. Plus 1/2 a t squared the same for the ball. Ah, different v zero. I'll say to save the one even though they're both initial, uh, t two plus 1/2 a t to square That should be a t one scrape. And now I know that they're Delta wise, his wife final minus y initial. But why initial is zero. So this just turns into why v zero It's this Be one here so I can say 12. He won, and now a is minus g. So that's 1/2 times minus nine point age times t one squared and our why over here his V one, which is 18 t two plus 1/2 again I have minus g T two squared. And now I know that however long the rock has been in the air, the ball has been in the air one second less because the ball is thrown a second later. Now I can say that if I just call ah t the time that the rock has been in the air, this transit to minus four point nine t squared. If I'm gonna call this tea, then the time for the ball is gonna be t minus one. This is throwing a second later, minus 4.9 times team minus one squared. And now we have wise and both. So we can set these two equal. So 12 T minus 4.9 t squared equals 18 T minus one minus 4.9. T minus one squared, and now we'll expand the right side. So this is gonna be 18 T minus 18 and now T minus one squared is T squared minus two t plus one. So we have minus 4.9 t squared and then minus Tucci. Attempts minus 4.9 is positive. 9.8 t and minus one times are plus one times minus 4.9 his minus 4.9. And now we have the T squared terms on both sides. Cancel. Now we have 12 T 18 t and 9.8 T, and so we end up getting 18. 4.9. If I combine all my terms, I get 22.9 equals 15.8 t. So t is 1.45 seconds. That's how long it takes for them to collide. Now, if I want to know, uh, the height I wish they collide. I can just plug back in here so I'll say why equals 12 times 1.45 minus 4.9 at 1.45 squared. And so why is 7.1 meters now? The next part instead of the rock being thrown first, the ball is thrown first so I can use the same system of equations that I have for the first part. Except I'm gonna say that the ball has Time T and the rock has Time t minus one because I'm just swishing the order of when their throne. So I can say what that Why for the rock is 12 times team minus one minus 4.9 T minus one squared and for the ball just becomes t. So why is 18 he minus 4.9 p squared, right? The only difference in this part is the times or different. Everything else is the same. Initial velocity acceleration. Ah, okay. So again, I can set these two equal, so 12 times T minus one minus 4.9 times T minus one squared equals the sworn. And now again, I'll expand out the left side this time. So I have 12 t minus 12 and same deal with this thing and expands the same way minus 4.9 t squared plus 9.8 t minus 4.9. Right now again, the T squared terms cancel out. So if I combine the's like terms and these, like terms, I get 3.8 e equals 16.9 and t equals 4.45 seconds. So that's the value we get for when they supposedly collide. However, if I plug in, plug into this one this time because it makes it easier, I say the why the height at which they collide is 18. It was 4.45 minus 4.9 times 4.45 squared. Then I actually get the height. That they collide is a negative number. And this means that since the ball is their own, first bull has the initial velocity of 18. If the ball is thrown first and then a second later, the rock is thrown. The rock will actually come down and hit the ground before the ball has to Clyde with. And so if there were no ground, then the ball would eventually catch up here that this is minus 16.9 meters. But since there's ground, they just both hit the ground and they never collide with each other.

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