1. Aim: How do projectiles differ when launched at an angle?
Angled Projectiles
Aim: How do projectiles differ when launched at an angle?

2. Vector Components Ax = A cos θ Ay = A sin θ
Two dimensional motion is where an object travels in the horizontal and vertical axes at the same time
However in order to simplify 2D problems you typically break the vector(s) into its x and y COMPONENTS (parts)
This is done using Trigonometry; and in most cases (not all)…
Ax = A cos θ
Ay = A sin θ
Horizontal Component
Vertical Component
Any Vector

3. Determine the horizontal and vertical components of the above vector
Example
50m/s
35°
Determine the horizontal and vertical components of the above vector

4. 2D Motion Problems
When dealing with 2D motion, always keep these important points in mind
When necessary, calculate the COMPONENTS of the 2D vector
A 2D vector usually has a MAGNITUDE and an ANGLE
NEVER use the 2D vector in ANY calculations besides determining the components
The values in the two axes are INDEPENDENT OF EACH OTHER
Horizontal values only affect horizontal values while vertical values only affect vertical values
NEVER MIX THE AXES!
However, TIME is the only value that can be used in BOTH AXES

5. Angled Projectiles
Angled projectiles combine INITIAL VERTICAL UPWARD MOTION and CONSTANT HORIZONTAL MOTION
All projectiles follow a PARABOLIC PATH
Launching the projectile at 45° will give the LONGEST RANGE (horizontal distance)
Launching the projectile at 90° will give the HIGHEST HEIGHT and LONGEST AIR TIME
Complimentary angles result in the same range but different times

6. Angled Projectile Rules
vy = 0m/s
tup = tdown θ
ttotal = 2×tup
vix = vi cosθ
ax = 0m/s2
Horizontal Velocity is Constant
viy = vi sinθ
ay = g = -9.81m/s2
The projectile STOPS at maximum height
The final vertical velocity is equal to the initial vertical velocity but in opposite direction

7. Example #1
A football quarterback needs to throw a 40m touchdown pass with 3 seconds left in the 4th quarter. Assuming he throws the ball at a 45° angle, how fast must he throw the ball?

8. Example #2
If Lionel Messi can kick a ball at a speed of 28.9m/s at an angle of 30°, (a) how high and (b) how long will it take the ball to reach maximum height?
(a)
(b)

9. Example #3
The M19 mortar has a muzzle velocity of 168m/s. If a shell were to be fired at an angle of 50°, (a) how high will the shell reach and (b) how far will it land? (a)

10. Example #3
The M19 mortar has a muzzle velocity of 168m/s. If a shell were to be fired at an angle of 50°, (a) how high will the shell reach and (b) how far will it land? (b)

11. SUMMARY How do you calculate the components of 2D vector?
Describe the path an angled projectile takes
What angles provide the…
Longest range?
Longest hang time?
List the horizontal and vertical rules for angled projectiles
What is the vertical velocity and acceleration at the pinnacle of an angled projectile?