1. Analysing projectile motion

2. Starter
What can you say about the motion and paths of the red and yellow balls in the picture?

3. Learning objectives Describe the force(s) acting on a projectile.
Explain the trajectory of a projectile.
Solve resultant vectors for projectiles.

4. Success criteria
Describe how the angle of trajectory of a projectile affects it’s range. (Grade C)
Use scale diagrams to calculate resultant vectors (Grade C-B)
Use Pythagoras’ theorum to calculate resultant vectors (Grade A)

5. Force on a projectile
After being released (and if we ignore air resistance), only one force acts on a projectile. What is it?
Gravity

6. Describe how the range of the projectile varies with the angle it is launched from. Can you explain this?
Gravity causes the projectile to decelerate as it goes up, and accelerate as it falls. The horizontal distance moved is the range. No force acts on the horizontal motion

7. Practical
Experiment P5c4 - old course

8. Resultant vectors
Velocity is a vector – it has magnitude and direction.
The resultant is the sum of the horizontal and vertical components.

9. Resultant vectors We can use Pythagoras’ theorem to solve:
v2 = vH2 + vV2

10. Resultant vectors
For a ball where vH = 12m/s and vV = 9m/s v2 = = 225 so v = 15m/s tan θ = 9/12= 0.75 so θ = tan = 36.9o The resultant vector is 15m/s at 36.9o to the horizontal

11. Now try these
A motorboat travelling 4 m/s, East encounters a current travelling 7.0 m/s, North. What is the resultant velocity of the motorboat?
A plane can travel with a speed of 80 mph with respect to the air. Determine the resultant velocity if it encounters a 10 mph crosswind.
A football travelling 5 m/s encounters a cross wind of 2.5 m/s. What is the resultant velocity of the ball?

12. Answers
V = 8.06m/s
θ = 60o
80.6 mph
θ = 7.1o
5.59m/s
θ = 26.6o

13. Learning objectives Describe the force(s) acting on a projectile.
Explain the trajectory of a projectile.
Solve resultant vectors for projectiles.

14. Success criteria
Describe how the angle of trajectory of a projectile affects it’s range. (Grade C)
Use scale diagrams to calculate resultant vectors (Grade C-B)
Use Pythagoras’ theorum to calculate resultant vectors (Grade A)