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Kinematic in Two and Three Dimension;Vector - Coggle Diagram
Kinematic in Two and Three Dimension;Vector
Vectors and Scalars
A vector has magnitude as well as direction.
Some vector quantities: displacement, velocity, force, momentum
A scalar has only a magnitude.
Some scalar quantities: mass, time, temperature
Addition of Vector(Graphical Method)
Subtraction of Vector, and Multiplication of Vectors by a Scalars
Then we add the negative vector.
Then we add the negative vector.
A vector V can be multiplied by a scalar c; the result is a vector cV that has the same direction but a magnitude cV. If c is negative, the resultant vector points in the opposite direction.
Adding Vectors by Components
Any vector can be expressed as the sum of two other vectors, which are called its components. Usually the other vectors are chosen so that they are perpendicular to each other.
If the components are perpendicular, they can be found using trigonometric functions.
The components are effectively one-dimensional, so they can be added arithmetically.
Adding Vector
Choose x and y axes.
Resolve each vector into x and y components.
Calculate each component using sines and cosines.
Add the components in each direction.
To find the length and direction of the vector, use:
Draw a diagram; add the vectors graphically.
Unit Vector
Unit vectors have a magnitude 1.
Using unit vectors, any vector can be written in terms of its components:
Vector Kinematics
Using unit vectors, any vector can be written in terms of its components:
Projectile Motion
A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola.
The speed in the x-direction is constant; in the y-direction the object moves with constant acceleration g.
If an object is launched at an initial angle of θ0 with the horizontal, the analysis is similar except that the initial velocity has a vertical component.
Projectile motion is motion with constant acceleration in two dimensions, where the acceleration is g and is down.
Solving Problems Involving Projectile Motion
Draw a diagram.
Choose an origin and a coordinate system.
Decide on the time interval; this is the same in both directions, and includes only the time the object is moving with constant acceleration g.
Examine the x and y motions separately.
Read the problem carefully, and choose the object(s) you are going to analyze.
List known and unknown quantities. Remember that vx never changes, and that vy = 0 at the highest point.
Plan how you will proceed. Use the appropriate equations; you may have to combine some of them.
Relative Velocity
We have already considered relative speed in one dimension; it is similar in two dimensions except that we must add and subtract velocities as vectors.
Each velocity is labeled first with the object, and second with the reference frame in which it has this velocity.
Here, vWS is the velocity of the water in the shore frame, vBS is the velocity of the boat in the shore frame, and vBW is the velocity of the boat in the water frame.
The relationship between the three velocities is:
