1. Non-Horizontally Launched Projectiles
Fired at an angle…
Have some Velocity in each direction
There is some velocity in the x-direction
And some velocity in the y - direction
Vy = vertical velocity
Vx = horizontal velocity

2. Non-Horizontally Launched Projectiles
30 degrees
60 degrees
Shot closer to horizontal
So horizontal velocity greater than vertical velocity
Vx > Vy
Shot closer to vertical
So vertical velocity greater than horizontal velocity
Vv > Vx Vy Vy Vx Vx

3. Non-Horizontally Launched Projectiles
Angle for Max Time in the Air?
Time in the air only affected by vertical direction
Launch angle should maximize velocity in the vertical direction
Launch angle for max time in the air – 90 degrees
Vy = maximum amount Vx = 0 !!
All velocity is in the y-direction
No velocity in the x

4. Non-Horizontally Launched Projectiles
Maximum Range – max horizontal displacement
dx must be the biggest number
So we want Vx and time to be the biggest number possible…
But remember…
Range, dx = Vx * time of flight

5. Non-Horizontally Launched Projectiles
Maximum Range – max horizontal displacement
dx must be the biggest number
So we want Vx and time to be the biggest number possible…
But remember…
If launch angle is zero – 0 – then…
Vx is at a maximum but time of flight is at a minimum
Range, dx = Vx * time of flight

6. Non-Horizontally Launched Projectiles
Maximum Range – max horizontal displacement
dx must be the biggest number
So we want Vx and time to be the biggest number possible…
So which is more important?
Horizontal Vx or vertical time of flight ? Neither!!
Max Range is at 45 degrees!!
Why???
Range, dx = Vx * time of flight

7. Non-Horizontally Launched Projectiles
Maximum Range – max horizontal displacement
At 45 degrees
Vx = Vy
Most of Vx and time
Of flight
Without sacrificing
one for the other
Range, dx = Vx * time of flight

8. Non-Horizontally Launched Projectiles
Relationship between 30/60 and 15/75
30/60 (and 15/75) have equal displacements because…
Range, dx = Vx * time of flight

9. Non-Horizontally Launched Projectiles
30 degrees
60 degrees
Shot closer to horizontal
Vx of 30 degrees = Vy of 60 degrees
and…
Vx of 60 degrees = Vy of 30 degrees…
So… ratio of Vx and time of flight is the same
dx is the same!
Shot closer to vertical Vy Vy Vx
THEY ARE THE SAME TRIANGLE!!!! Vx