2D Kinematics

2-D Motion can be described as the combination of…

…the separate x and y motions

The x-direction is describing…

…horizontal motion

The y-direction is describing…

…vertical motion

Projectile

any object that moves through the air, or through space, acted on only by gravity

Projectile motion is a 2D free-fall motion under the influence of only…

…gravity

In 2D motion problems…

…air resistance is neglected AND projectiles in 2D follow a parabolic trajectory

Projectile motion is made up of _ independent 1D motions

2

What are the two 1D independent motions that make up projectile motion?

Free fall motion (in the vertical direction) and uniform motion (in the horizontal direction)

In the y-direction, the objects in projectile motion move with…

…constant acceleration (a_y = -g)

In the x-direction, the objects in projectile motion move with…

…constant speed (a_x = 0)

In projectile motion, the _ velocity never changes

horizontal

In projectile motion, the _ velocity decreases by 9.8_m/s every second as the object rises

vertical

At the peak of the projectile motion parabola, there is only _ velocity

horizontal

Velocity components (equation):

v_x = vcos(0), v_y = vsin(0)

Projectile’s speed (equation):

v = square root (v²_x + v²_y)

Direction of motion (equation):

0 = tan^-1(v_y/v_x)

Launch

The start of a projectiles motion

Launch angle

The angle of initial velocity above the x-axis

Level horizontal range R

The horizontal distance traveled by a projectile that lands at the same level it started

Is vertical motion the same or difference if an object were thrown straight up/straight down with the same initial y velocity?

The same; vertical motion is symmetric for an object thrown upward/downward with the same initial y velocity.

The range of a projectile reaches maximum at a launch angle of _ degrees

45 degrees