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Apologia Physics M4

Motion in Two Dimensions

QuestionAnswer
By adding displacements, we can get overall displacement.
We approach two-dimensional problems by looking for the one-dimensional part of the problems.
When a projectile is fired at an angle relative to the ground, its motion is called parabolic.
Parabolic means it follows the curved path of a parabola.
When we look at the components of a vector, we really have the vector itself.
Once a cannonball leaves the cannon, the only things acting on it is gravity,
Gravity only acts in the y-dimension.
Gravity does NOT affect the x-component of velocity.
The x-component of velocity NEVER changes.
The x-component of the velocity vector stays exactly the same length and points in exactly the same direction for the entirety of the flight of the object.
In the middle of a cannonball's trip, gravity has reduced the y-component of the ball's velocity to zero.
When the velocity is point in the same direction as gravity's pull, the y-component of the velocity increases, making the object fall even faster.
Parabolic motion is motion that occurs when an object moves in two dimensions but has zero acceleration in one of those dimensions and a constant, non-zero acceleration in the other.
When a projectile reaches its maximum height, the y-component is zero.
A projectile will land with the exact opposite velocity to what it started with.
The speed of a projectile is the same when it lands as it was when it launched.
The projectile reaches it maximum height at the midpoint of its journey.
The range equation from this module ONLY applies when the target/end point is at the same level as the origin point of the projectile.
We are also neglecting to take air resistance into account throughout this discussion.
We are calculating the range of a projectile when we determine the distance that it travels in the x-dimension.
initial speed = Vo
To determine the y-component of a projectile, we use Voy=Vo*sin(O) O=angle
If we know the initial velocity in the y-dimension, we can calculate the time it takes for the projectile to reach its maximum height.
g= gravity
range = {original velocity squared * sin (2*angle)] / gravity (Equation 4.9)
Equation 4.9 ONLY applies to projectiles that land at the same height from which they are launched.
In order to remove a function from one side of an algebraic equation, take the inverse of the sign from both sides of the equation.
Conventionally speaking, a positive sign means upward motion.
Conventionally speaking, a negative sign means downward motion.
When we are looking at a situation in which the end point is different in height from the starting point, we need to find another way to solve the problem.
When starting and ending height are different, we may have to solve for the y-dimension and then use the information to solve for the x-dimension (or vice versa).
Created by: MrsHough
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