- Kinematics equations for vertical, horizontal, and oblique projection are used to describe the motion of an object that is projected into the air under the influence of gravity.
- The equations take into account the initial velocity and direction of the object, as well as the acceleration due to gravity, to determine the position and velocity of the object at any given time.
Vertical Projection:
- When an object is projected vertically upwards, it follows a parabolic path. The equation of motion for a body projected vertically upwards is
x = x0 + v0t - (1/2)gt^2
Where:
x is the final height of the object at time t.
x0 is the initial height from which the object was projected.
v0 is the initial velocity with which the object was projected.
g is the acceleration due to gravity (9.8 m/s^2 on the surface of the Earth).
t is the time elapsed.
Horizontal Projection:
When an object is projected horizontally, it follows a straight line path. The equation of motion for a body projected horizontally is:
x = x0 + v0t
- Where:
- x is the horizontal displacement of the object at time t.
- x0 is the initial horizontal displacement of the object at time t=0.
- v0 is the initial horizontal velocity with which the object was projected.
- t is the time elapsed.
Oblique Projection:
When an object is projected at an angle, it follows a path that is a combination of vertical and horizontal motion. The equations of motion for a body projected obliquely are:
x = x0 + v0t cosθ - (1/2)gt^2
y = y0 + v0t sinθ - (1/2)gt^2
Where:
- x is the horizontal displacement of the object at time t.
- y is the vertical displacement of the object at time t.
- x0 is the initial horizontal displacement of the object at time t=0.
- y0 is the initial vertical displacement of the object at time t=0.
- v0 is the initial velocity with which the object was projected.
- θ is the angle at which the object was projected.
- g is the acceleration due to gravity (9.8 m/s^2 on the surface of the Earth).
- t is the time elapsed.