Projectile Motion

The javelin is an excellent example of a projectile. Once it leaves the thrower's hand, the only forces acting on it are air resistance and gravity. This fact allows us to use the kinematics equations to model its path through the air. In our examples we will be ignoring air resistance to simplify matters.

Goals

Be able to describe position, velocity and acceleration as two-dimensional vectors.
Recognize two-dimensional projectile motion as simultaneous one-dimensional motion in two directions.
Use the one-dimensional kinematics equations to solve projectile motion problems with constant acceleration.

Definitions

Projectile

Any body which is in freefall that has a horizontal aspect to its motion.

Trajectory

The curve which describes the motion of a body in space.

Motion in Two Dimensions

Even though we are working in two dimensions, we can use the same principles to solve projectile motion problems. It turns out that the x and y components of motion are completely separable. This movie shows the independent motion in two directions. Notice that even though the ball on the left is moving horizontally, it still falls at the same rate as the one on the right.

At any time, a projectile's velocity can be divided up in the following fashion.

After we have everything in terms of x and y we may use the one-dimensional kinematics equations to solve any projectile motion problem.

Summary of Projectile Motion Equations

Remember that these are the same as the kinematics equations that you used for one-dimensional motion.

Component of Motion	Equation
X Acceleration
Y Acceleration
X Velocity
Y Velocity
X Position
Y Position

Example 1

The javelin thrower above releases the javelin 1.50 meters from the ground at an angle of 48°. If the initial velocity of the javelin is 25.00m/s, what is the distance that the javelin travels.

Example 2

Find the maximum height of the javelin and it's velocity vector on impact.