1. Final vertical velocity?
Do Now:
Given an initial velocity of 30 m/s off a cliff 120 m high, what is his time of flight?
Distance travelled?
Final vertical velocity?

2. Aim: How can we calculate the total time and distance traveled?
HW: WS

3. Sketch the path described
Fire Away!!!
Sketch the path described

4. Projectile Vector Diagram
vy at top = 0
Parabolic Path
ax = 0
What are some assumptions?
ay = m/s2
vfy = -viy

5. Vertical Axis: Y Which assumptions can we make?
Initial velocity (viy = vi sin θ)
Acceleration due to gravity = m/s2
At max height vfy = 0m/s
Time to max height = ½ total time in the air
When the projectile lands, vfy = -viy

6. Horizontal Axis: X Which assumptions can we make?
Initial velocity (vix = vi cos θ)
acceleration = 0m/s2
Horizontal velocity is CONSTANT!
Maximum Range = vix × total flight time

7. Components Activity Use Soh Cah Toa to calculate x and y.
Where have we seen this before?
V= 50m/s
viy
30° vx

8. 1. A soccer ball is kicked with a velocity of 15 m/s at an angle 30 degrees above the horizontal. 2. A player in the outfield throws a baseball in the air 45o above the horizontal at a speed of 25 m/s. 3. A golf ball is clubbed 35 degrees above the horizontal with a velocity of 20 m/s.

9. Making it easy!
STEP 1: Always break initial velocity into it’s vertical and horizontal components first!!!
Why?
Once we do this, it becomes a simple 1D question for any unknown!
We can use all our kinematics equations as usual, BUT only with variables in the same direction!!!

10. Wrapping it up!
A soccer ball is kicked with a velocity of 15 m/s at an angle 30 degrees above the horizontal.
We must work in specific directions!
Determine the horizontal and vertical components of initial velocity.
Calculate the maximum height the ball reaches
Calculate the time it takes to reach max height
Find how far the ball lands from the player

11. Summary What is the horizontal component for initial velocity?
What is the vertical component for intial velocity?
What are assumption for the vertical direction of motion?
Assumptions for horizontal direction?