eloquent logic - vector kinematics

Legend

l	=	distance
t	=	time
v	=	speed/ velocity
V_av	=	average speed
l	=	change in distance
t	=	change in time
v	=	Change in velocity
V_f	=	final velocity
Vi	=	initial velocity
t_i	=	initial time
t_f	=	final time
a_av	=	average acceleration
d	=	distance

Projectile Motion

A projectile's sideways-upward movement can be imagined as if it were two simultaneous independent motions: a horizontal flight (ideally at constant speed) and a vertical gravity fall (ideally at constant acceleration). The gravitational interaction causes a vertical acceleration, but no such influence exists horizontally, and the horizontal acceleration (ignore air resistance) is zero.

The shape of the arc traveled by a projectile can be approximated by forming an equation relating is horizontal and vertical displacements.


		Here, the the cork is shot out of the bottle. The red arrow is the vertical component of the cork's path. The blue arrow is the horizontal component of the cork's path. Notice how the red arrow is decreasing until it reaches the top and becomes a downward arrow. The blue arrow remains constant (ignore air drag). Recall from basic concepts of vector kinematics, the arrow's resultant path becomes the green arrow.

The green arrow becomes the path of the cork, the projectile motion. The red arrow changes due to gravity.
Note the shape of the path followed is a parabola.

Acceleration

Interactive Lab