>y=ut sin(a)-1/2gt²
The equation y=utsin(θ)−
2
1
gt
2
describes the vertical position (or displacement) of a projectile at any given time t , assuming the upward direction is positive.
In this formula:
u is the initial velocity magnitude.
θ (often denoted as 'a') is the angle of projection relative to the horizontal.
g is the acceleration due to gravity (approximately 9.81m/s
2
).
t is the time elapsed since projection.
The term utsin(θ) represents the vertical displacement if gravity were absent, while the term −
2
1
gt
2
accounts for the downward pull of gravity acting on the projectile. This equation is a specific component of the full projectile motion trajectory, derived from the general kinematic equation y=u
y
t+
2
1
a
y
t
2
, where the initial vertical velocity u
y
is usin(θ) and the vertical acceleration a
y
is −g .