Physics lesson grade 10

Two Dimensional Motion
The position of an object in two dimensional motion can be described completely if we use two coordinates, which are symbolized by x coordinate (horizontal) and y coordinate (vertical). The examples of two dimensional motion are projectile motion and circular motions.

Projectile Motion

Based on the path of a projectile shot above, there are two independent one-dimensional motions:

Motion with an uniform velocity in the horizontal direction since the projectile doesn't sense any acceleration to the horizontal direction
Motion with an uniform acceleration in the vertical direction since the projectile senses a downward gravitational acceleration

The equations of Projectile Motion

Initial speed of the projectile:

In horizontal direction:

In vertical direction:

Speed of the projectile at a certain time:

In horizontal direction:

In vertical direction:

Position of projectile at certain time:

In horizontal direction:

In vertical direction:

Maximum height

The time required by the projectile motion to arrive the peak of its path is:

The maximum height:

Range and Maximum Range

The total time is:

The range of the projectile is:

The maximum range of the projectile is:

Parabolic path
Because the path of the projectile satisfies a parabolic equation, we can also say the motion of a projectile is parabolic motion

The parabolic equation:

Circular Motion

Circular motion can be defined as a motion of an object through a circumference of a circle.

Uniform Circular Motion

Uniform circular motion is the motion of an object traveling at a constant (uniform) speed on a circular path.

The formulas are:

T (period) : Time required to complete one circular motion

r : radius

Ω : Angular velocity (rad/s)

Ɵ can be displaced in radian (rad), angle (degrees), cycle

Kinematic Circular Motion Equations

Centripetal Acceleration

Acceleration is always directed to the center of the circle. Magnitude ac of the centripetal acceleration depends on the speed of the object and the radius of circular path . The equations are: