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A batter hits a baseball at a speed of 35.0 $\mathrm{m} / \mathrm{s}$ and an angle of $65.0^{\circ}$ above the horizontal. At the same instant, an outfielder 70.0 $\mathrm{m}$ away begins running away from the batter in the line of the ball's flight, hoping to catch it. How fast must the out fielder run to catch the ball? ( (ignore air resistance, and assumethe fielder catches the ball at the same height at which it left the bat.)

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4.0 $\mathrm{m} / \mathrm{s}$

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

University of Michigan - Ann Arbor

Hope College

McMaster University

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.

03:48

A batter hits a fly ball w…

05:24

08:09

04:36

02:36

04:28

A ballplayer standing at h…

02:12

A batter hits the baseball…

04:22

A baseball is hit into the…

07:16

At $t=0$ a batter hits a b…

05:35

A batted baseball leaves t…

11:55

A ball player hits a home …

A baseball is hit directly…

so here the initial equals 35 meters per second. The baseball is hit with initial velocity of 35 minutes per second at an angle of 65 degrees above the horizontal. So it's a fly ball and ah, we can say that Delta Y equals zero meters. We're going to assume that the baseballs changing height does not change, given that it is ah, hit at a certain height and then it is catch and it is caught at that same exact height, given that most baseball players have the same height. So we can say that if delta y equals zero, we can say that our is going to be equal to the initial squared sine of tooth Ada divided by G. And this is going to be equal to 35 squared times sine of 130 degrees, divided by 9.8. And this is giving us not 95.76 meters now. The player is the player is at 70 meters, so we can say that the exposition of the player is equaling 17 years away from home plate again. The origin is simply home plate and the time it takes is going to be equal to two times the initial sign of data divided by G, So this will be equal to two times 35 sign of 65 degrees divided by 9.8, and this is equaling 6.474 seconds. So essentially the velocity needed by the player is going to be equal to Delta X, divided by Delta t. So this would be, Ah, 70 minus 95.76 meters, divided by six point 474 seconds, and this is giving us negative 3.98 meters per second. Now, mind you, this is the velocity and the velocities only negative in this case because it is Ah, the the baseball player is moving away from home plate and home plate is the origin. So if you're moving away from the home plate, you have ah, negative velocity. If you wanted to be. If you saw on Lee one of the magnitude, you could say that his speed but the speed needed is going to be 3.98 meters per second. But again, you should specify that the player has to move backwards in order to catch this ball. That's the end of the solution. Thank you for watching

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