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MMH A soccer player kicks the ball toward a goal that is 16.8 m in front of him. The ball leaves his foot at a speed of 16.0 m/s and an angle of 28.0- above the ground. Find the speed of the ball when the goalie catches it in front of the net.

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Physics 101 Mechanics

Chapter 3

Kinematics in Two Dimensions

Motion in 2d or 3d

University of Michigan - Ann Arbor

University of Washington

Hope College

University of Winnipeg

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.

04:23

A soccer player kicks the …

02:24

As an aid in working this …

05:59

. As an aid in working thi…

06:01

A soccer player takes a fr…

04:25

$\cdots$ In a soccer game …

01:05

A soccer goal is 2.44 m h…

04:12

A soccer ball is kicked fr…

01:36

A football player kicks a …

15:36

08:52

$\bullet$ A player kicks a…

02:52

A soccer player can kick t…

02:57

So the question states that a person kicks a soccer ball at 16 meters per second, an angle of 28 degrees, and a goalie catches a ball that 16.8 meters away. And we're trying to find what the velocity of the ball is when the goalkeeper catches it. So the first thing we really should do is break up this initial velocity vector into components so into a V of X and a V of why component we confined Visa Becks, because we know that co sign of 28 degrees is equal to, uh, adjacent over iPod knees and the adjacent. In his case, his visa vex. So Visa backs over 16 which means Visa. Becks is equal to 16 co sign 28 degrees, and the same thing goes for resupply. Except instead of a co sign. It's a sign so we'll get that pizza. Why is equal to 16 times sign of 28 degrees? So now that we know this, uh, we should try and find how long the ball is in the air. Four. So to do this, we can take our visa, Becks. And because there's no acceleration in the X direction. We can multiply it by t, and this will give us our displacement in the X direction. So there's no acceleration term in this formula. So when we plug in Visa, Becks and Delta X, which is 16.8 meters, we find that T is around 1.1891 seconds. And so this is gonna be important when solving for, um, our vertical component of the velocity. So if we if we look at the final velocity of the ball when the goalkeeper catches it, we know for effect that the horizontal component of the velocity is going to stay constant because it's project out motion. There's no acceleration, as we said earlier, so the horizontal velocity is going to be 16 times co sign of 28 degrees. Now, of course, we're trying to find the vertical component eso weaken, solve for the total velocity of the bomb. Now that we know the time, we can just use a cinematic equation to solve for this vertical lost e. So we're going to use the one that states that the final velocity is equal to the initial lost E plus the acceleration times the time so you don't know what the final US is. We know that the initial velocity in the vertical direction is 16 times sign of 28 degrees. We also know that the acceleration is equal to negative 9.8 meters per second squared due to gravity. And we also know the Time T is 1.18 91 seconds. So when we saw for V, we get that he v should really be visa. Why? Which is this question? Mark is equal to negative 4.14 to 6 meters per second. And now all we really have to do is protect your in here in the salt for this Capital V Here. Um, when we work out 16 times coastline of 20 degrees, we get that visa of ex is equal to 14.12716 meters per second. And now that we know Visa, Becks and Visa, why weaken Take thes square root of visa X squared plus visa y squared. This will just give us our capital V and when we put this in, we find that capital V is equal to 14 0.72 meters per second

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