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A golfer hits a shot to a green that is elevated 3.0 m above the point where the ball is struck. The ball leaves the club at a speed of 14.0 m/s at an angle of 40.0 above the horizontal. It rises to its maximum height and then falls down to the green. Ignoring air resistance, find the speed of the ball just before it lands.

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Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

Rutgers, The State University of New Jersey

University of Washington

Simon Fraser University

University of Sheffield

Lectures

04:01

2D kinematics is the study of the movement of an object in two dimensions, usually in a Cartesian coordinate system. The study of the movement of an object in only one dimension is called 1D kinematics. The study of the movement of an object in three dimensions is called 3D kinematics.

10:12

A vector is a mathematical entity that has a magnitude (or length) and direction. The vector is represented by a line segment with a definite beginning, direction, and magnitude. Vectors are added by adding their respective components, and multiplied by a scalar (or a number) to scale the vector.

02:46

A golfer hits a shot to a …

03:37

04:05

A golfer tees off from the…

05:08

03:32

(a) A projectile is launch…

02:09

A golfer, standing on a fa…

02:53

A golfer hits a shot to an…

04:17

MMH A golfer, standing on …

10:15

A golf ball with an initia…

01:22

A Record Golf Stroke The f…

02:38

A 47.0-g golf ball is driv…

okay. You were in the er the golf question, Probably 20. So first we know it's protect our question. So which is she? Wished I was dropped her angle. This is a right angle, even though it doesn't look like it. Uh, sir, Angle theater. And it's 40 degrees. We have, ah, initial velocity along the part news 14 meters per second and from Trig, we're gonna be able to find this is our Y side. And this is very excited. So we're gonna have our excite to be V. I co signed a feta because pro signed deals with the X here, and X is the ground which is adjacent to the angle. So it means one is gonna be signed it Sylvie, I sign data because signed deals with the why the opposite side of where we're headed. So perfect? Um, no, it could set up A few equations we know are lost in the ex Direction is going to be equal to our initial velocity times the coastline of feta. So that's equal to 14 sorry meters per second co sign of 40 degrees and we're getting initial velocity in the acts of 10.72 meters per second. Okay, so now we can use a Why question? We don't know the time for, like the vertical equation. Uh, do you know how high? Why is it said? Why this side is able to three meters above the ground? This is three meters above the ground here in the life site s We're gonna use thief cinematics formula uh, yesterday. Wade Burke, you groovy squared. Why equals initial velocity and the why plus two a y times. Why? So this is really just equal. We know that. Why people thio are the bosses and the wise able to v i same theater. What? We have to square that all on. Then we have to subtract minus two g y cause acceleration here due to gravity. So that's G y. Uh Okay, so perfect. Now we have everything that we need so we can just plug in number. So we have 14.0 meters per second sign off 40 degrees squared minus two you times 9.80 meters per second squared time there. Why direction which was three meters. And this gives us a final squared velocity on the way of 22.18 two meters squared per seconds. Word. So if you take the square root of that, we can fine of lost in the line. But that's not gonna help us, because the next part, we're gonna find the magnitude of the final velocity. And so if we square, this is pretty much when we go, Ah c equal squared a squared plus B squared. These units are already squared so we don't have to square this again when we put it out for you because he's a really good so go. So the magnitude of the final velocity is equal to this which is equal to the front of lost. He scored in the X and the final loss he scored in the Why is your including both angles from where the ball's coming down. So you were gonna have the square root of 10.7 to you meters per second and we swear that and then remember like we said from the last light, we don't have to square. This one is very squared. So plus 22.182 meter squared per second squared and then stick the scared of all that and we get a fun of lost any of 11.71 meters per second. So that's how fast it's going when it hits the green. All right, Thank you for watching.

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