Youtor
2D Kinematics amp Projectile Motion
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=eXq9tCiLTDg
In this video we cover 2d kinematics and projectile motion. • 0:00 - Position, Displacement, and Velocity in 2D • 1:51 - Acceleration in 2D • 4:00 - Directions of Velocity and Acceleration • 6:14 - Projectile Motion • 7:50 - Kinematic Equations in 2D • 9:00 - Range in Projectile Motion • 11:49 - Things to Remember • Position, displacement, velocity and acceleration in two dimensions are all defined in the same way as in one dimension. However, now all of these vector quantities have both x- and y-components. This means we can use our knowledge of vectors. • We need to be aware of the relative directions of velocity and acceleration. In one-dimension, velocity and acceleration are either parallel in the same direction, or antiparallel in opposite directions. In two-dimensions, the acceleration can be perpendicular to the velocity. In this case, rather than the speed changing, the direction of velocity changes. We can also have acceleration that is both perpendicular and parallel to the velocity. In this case both the speed and direction of velocity will change. • Projectile motion is an example of constant acceleration where an object moves only under the influence of gravity. Because gravity only acts downward to accelerate objects toward the center of the earth, there is no acceleration in the x-direction and the y-component of acceleration is the same as in freefall, gravitational acceleration downward in the -y-direction. • We can take these acceleration values and plug into kinematic equations, or constant acceleration equations. Doing this we find that the x-component of velocity remains the same, and there is only one equation that describes the horizontal motion. In the y-direction we get the same five kinematic equations as in freefall motion. • In projectile motion, if an object lands at the same height as it was launched, we can find an equation for the horizontal distance traveled. This horizontal distance traveled in called the range of the projectile. Here we find the range depends on the initial speed and angle the projectile was launched. Changing the speed obviously will affect the range, but for a give initial speed the maximum range is reached when the angle is 45 degrees. This gives the projectile enough hang time or time of flight while also giving it enough initial horizontal speed to travel the furthest distance. Larger angles will just make the projectile go higher but not as far horizontally. Smaller angles will mean the projectile will not spend much time in the air and quickly hit the ground. • There are many things worth remembering when looking at projectile motion. First, projectile motion is an extension of freefall, so everything that we already know and look for in freefall will apply and should be remembered. Next, we need to look at the motion in either the x-direction or y-direction at a time. Because at any time the object is both moving in x- and y-directions, time is what connects the two directions of motion. We can use kinematic equations to find information about the x- and y-components, and then use what we know about vectors and right triangles to recombine these components. • Using Pythagorean theorem and inverse tangent we can combine x- and y-components of vector quantities to find the magnitude and direction of these quantities at some point along the object's trajectory or path.
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