2 Dimensional Motion
"When you have eliminated the
impossible, whatever remains, however improbable, must be
the truth"
Arthur Conan Doyle – The Sign of Four (1890)
·
In three dimensions the
position of a particle is described by its position vector, r, where r
= ix + jy
+ kz.
The instantaneous velocity and acceleration are given by
Average velocity and average acceleration are defined by
Note that the instantaneous and average velocities are not necessarily in the same direction, similarly for the instantaneous and average accelerations. In particular, note that if v2 and v1 have the same magnitude (constant speed) then acceleration is not zero if the directions of v2 and v1 are different.
Acceleration can be
caused by change in magnitude or direction of the velocity of
a particle.
·
Projectile
Motion:
Limiting ourselves to motion in 2 dimensions (horizontal - x and vertical – y) and considering constant acceleration in y, ay = -g, and zero acceleration (constant velocity) in x, we can extend the kinematic equations as follows,
· These equations describe the motion of a projectile and lead to the conclusion that such an object moves in a parabolic path. The parabolic nature of this motion, courtesy the University of Virginia, is demonstrated here.
.
“
John Updike – Picked up Pieces (1976)
Dr. C. L. Davis
Physics Department
University of
email: c.l.davis@louisville.edu
