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A gun shoots a shell into the air with an initial velocity of $100.0 \mathrm{m} / \mathrm{s}, 60.0^{\circ}$ above the horizontal on level ground. Sketch quantitative graphs of the shell's horizontal and vertical velocity components as functions of time for the complete motion.

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Physics 101 Mechanics

Chapter 3

Motion in a Plane

Physics Basics

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

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.

01:05

Projectile Motion A gun wi…

08:53

On level ground a shell is…

06:29

0:00

06:10

05:07

Projectile motion A gun wi…

02:46

VELOCITY A gun with a muzz…

01:20

01:41

A gun with muzzle velocity…

so we know that the initial equals 100 meters per second and we know that the angle of launch equals 60 degrees. So we can say that the ex initial equals V X Final, because again, there's no acceleration the ex direction because the bullet is in free fall the entire time so we can say 100 co sign of 60 degrees. And this is simply going to equal 15 meters per second. If you want to draw a graph of this, it's pretty simple. We simply have tea in seconds on the X axis and then on the y axis we havethe e x velocity, the X component of velocity and meters per second. It would simply be a straight line where this would be 50 now for ve y final. However, view our final is a bit different. Viv are final equals V y initial plus GT. We know that view initial equals. Rather, we can say ve y final equals 100 sign of 60 degrees plus a rather minus 9.8 t. And so we can say that V why final simply equals 86.6 minus 9.8 t. So in order to see what this would look like. You have essentially this. This would be the why access. So why? Component of velocity and meters per second. And then we can draw the X axis in the middle. This would be in t seconds, and it would simply be a straight line going down like that. Ah, maybe a bit more steep there. Yah! And where we have Ah slope essentially of negative 9.8. Because with every second it's the philosophy the Y direction decreases 9.8 meters per second. So and then here it starts at the why intercept. So 86.6. And I would simply go down from here. Where this if this were to equal the ah halfway mark. So essentially the if this were a mark. Why Max? We can say that this ending hear when it hits the ground, it's going to be negative 86.6. And that's the end of the solution. Thank you for watching

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