When solving planar motion problems every acceleration gets list of givens. For motion in 2 dimensions, this means a list of givens for the vector variables that point horizontally and a list for variables that point vertically. Each column is its own kinematics problem. Time is the only variable that same value for each givens' column. Everything else is not shared between the columns. To find the position of an object, calculate its horizontal position and its vertical position at the same instant in time. To find an objects direction, calculate the horizontal and vertical velocities and then combine them using trigonometry. To find the time an object is in the air use either column of givens and the kinematics equations. This is because time is the only kinematics vector that is not a vector.
Projectile Motion and Planar Motion
A projectile is any object that moves through the air without guidance. For an introductory physics class, air resistance will be ignored unless stated otherwise.
A basketball thrown towards a basketball hoop.
A baseball pitched to a catcher.
A football being thrown or kicked.
A person falling out of a tree.
An arrow being shot from a bow.
A penny tossed off a tall building.
Examples of objects that are NOT projectiles because they control their flight path while in the air.
An airplane flying through the air
A helicopter flying through the air
A parachutist skydiving from a plane
A missile with an active guidance system. (This is a system were the fins adjust themselves in flight -rare in an introductory physics class.)
In planar motion, the horizontal motion and the vertical motion are independent from each other. The motion of a projectile is planar motion. By recognizing that the motion is projectile motion allows a physicist to make certain assumptions that will make finding answer easier.
Examine the motions of the three balls in the animation below.
Notice how each ball is moving at a different horizontal speed before the balls reach the edge of the table. Despite there different horizontal speeds, they each hit the floor at the same time. If the horizontal motion and the vertical motion were related to each other, then each ball would hit the ground at different times. But this does not happen. The fact that the horizontal and vertical motions are independent of each other will help to solve this as two kinematics problems.
Connecting Planar Motion with Projectile motion
Projectile motion is planar motion. There are two accelerations for projectile motion. Vertically, the pull of the Earth will accelerate all objects downwards at 9.80 m/s2. Horizontally, no forces will act on the projectile so it will always move at a constant velocity. This means that horizontally the acceleration is zero. For this an introductory physics class, there are never any forces acting on a projectile in the horizontal direction. The table of kinematics givens will like the one below with a list of given for each acceleration.
Table of givens
- 9.80 m/s2
A New Way to Look at the "Givens"
In planar motion problems the initial velocity was be given as 7 m/s to the left at a constant velocity and 2 m/s upwards with an acceleration of 9.80 m/s2 downwards.
In projectile motion the accelerations are implied from the fact that the problem is a projectile motion problem. The velocity is typically not given so neatly as in the previous statement. Instead the velocity is given as something like the image below.
This is can be made into a right triangle with vo as the hypotenuse. The embedded YouTube video below explains how to use trigonometry to find the horizontal and vertical components of the initial velocity.