1. Projectile Motion

2. Animation

3. Definition
Motion subject only to the force of gravity..we will ignore air resistance.
Accelerated uniformly in the vertical direction
Constant velocity in the horizontal

4. Objectives:
Calculate time of flight given initial velocity and launch angle
Calculate range
State the angle that results in maximum range for a given launch velocity.

5. Motion in two dimensions
Vertical and Horizontal
Equations are the same as in Kinematics:
Notice use of “y” for vertical motion and that there is no acceleration term in the horizontal equation.

6. Break it down into its components!
A projectile is launched at 30 deg angle with a velocity of 10 m/s
Decompose the velocity vector.
Now we can analyze each motion separately.

7. Write BOTH position equations
If the projectile lands 5 meters lower than is was launched…
Notice that the vertical equation can be solved…
t=1.64 or seconds

8. Substitute time back into the other eq’n

9. Method…
This general procedure can be applied any time your are given the launch angle and velocity.
Decompose the velocity vector
Write both position equations
Solve one for time
Substitute time into the other equation

10. You can also solve for… Velocity components at any point in time:
The angle of its flight path from horizontal:

11. Another type What is the maximum height a projectile will reach?
No time given….

12. continued
At max height its vertical velocity is zero…just for an instant!

13. Range equation
With mild algebraic discomfort and a few trig identities, you can solve the general equations given the projectile lands at the height it was launched…
Notice the total velocity is used
By inspection…you can determine the angle that will result in max range…

14. The most common problem on AP exams
An object rolls of the edge of a table with a certain speed. The table is so tall…how far from the edge of the table will it land?

16. Summary Four steps Range Equation only for level ground Decompose
Both position eq’ns
Solve one
Substitute time into the other
Range Equation only for level ground
45 deg