Oblique projectile motion (Left), Horizontal projectile motion (Middle), Projectile motion on an inclined plane (Right)
Kinematic quantities of projectile motion The magnitude of the displacement:
Where, r x2 y2
X axis is horizontal and Y axis is vertical. The maximum height of projectile
sin θ is the component along y-axis v 0 2 sin2 ()
cos θ is the component along x-axis
V0 is the initial Velocity,
It is a movement of an object along the
Vx is the velocity along x-axis circumference of a circle or rotation along
a circular path.
Vy is the velocity along y-axis
It can be uniform, with constant angular
g is the acceleration due to gravity and rate of rotation and constant speed, or non-
uniform with a changing rate of rotation.
t is the time taken.
Examples of circular motion include: an
artificial satellite orbiting the Earth at
constant height, a stone which is tied to a
rope and is being swung in circles.
Velocity in Circular Motion:
v r r
v x v 0 cos()
v y v 0 sin( ) gt Acceleration in Circular Motion:
The magnitude of the velocity d v2
v vx 2 vy 2
Where the angular rate of rotation is ω. (By
rearrangement, ω = v/r.) Thus, v is a constant,
Displacement and the velocity vector v also rotates with
constant magnitude b, at the same angular rate
At any time t, the projectile"s horizontal and ω.
x v 0 t cos( )
y v 0 t sin( ) gt 2