1. Vector addition allows us to consider movement in 2-D
Problems like moving across a river or other water navigation.
Flying with wind considerations.
Driving
PROJECTILES

2. The KEY to working with vectors:
Vectors that are at right angles are
INDEPENDENT.
This means that motion vectors that are at right angles to one another have no effect on each other.
This is true in all, but a few very special cases (e.g., magnetic fields).

3. The Bullet Problem
See transparency…

4. Projectiles
A projectile is any object that is shot/thrown into the air where it achieves free fall.
You MUST consider the fact that gravity will produce a constant downward acceleration on the projectile.
This downward acceleration DOES NOT affect the forwards/horizontal motion of the projectile.
We will ignore the effects of air resistance to projectile bodies in this course since it produces a non-constant acceleration, thus invalidating our kinematics relationships.

5. Vy=0 at max height
Vx is constant
Vyo
-Vyo
T1/2
T1/2
Sketch both the resultant velocity and the acceleration vector at each
indicated point on the model trajectory.

6. How to solve a projectile problem:
Depends on what information you are given:
If given initial velocity vector:
Break into x- and y-components, use y-direction to find time to max height and/or maximum height.
Double time calculated to find total flight time.
Use total flight time and initial (constant) x-velocity to find horizontal displacement.
Acceleration in the x-direction is ZERO!

7. If you know horizontal displacement (how far the thing went):
You need at least one other piece of information to solve the problem (i.e., time of flight or initial horizontal velocity).
You can work backwards using the method on the previous slide to find information about max height.
Remember, in this case, half the time of flight was spent for the projectile to rise in the air and the other half was spent falling.
Acceleration in the x-direction is still ZERO!

8. Nasty problem types:
What about when the projectile hits a wall either while it is coming up, or going down?
Again, horizontal acceleration is still ZERO, and you will have to work with what you are given to find things like max height, total flight time (also time up/down), and initial and final velocities.
In all cases, remember that your x- and y-directions are INDEPENDENT and that time is the only variable that links both systems.

9. Practice
A cannon is fired upwards at 35 degrees with an initial velocity of 62 m/s. Find the maximum height to which the projectile rises, total time in the air and range.
A cannon is at 22 degrees above the ground. 14 seconds later the round explodes 2426 meters downrange. Find the initial velocity of the cannonball and the maximum height of the projectile.
A soccerball is kicked from the ground with an initial speed of 19.5 m/s at an angle of 45 degrees. A player 55 m away begins running to meet the ball at the instant it is kicked. What must his speed be if he is to meet the ball just before it hits the ground? At what position from where it was kicked will it land?