Projectile Motion and Example Calculations

Projectile Motion

What is the projectile motion of a body?
- A body in projectile motion will move in two dimensions simultaneously. Bodies that are in projectile motion are resolved(divided) into two components. A vertical component(Vy) and an horizontal component(Vx). These components however are dealt with simultaneously.


Please refer to the diagram below showing projectile motion.

Projectile motion

Formulas associated with projectile motion include:

• Vy = VsinA
• Vx = VcosA
• V = Sqrt [Vy^2 + Vx^2]
• TanA = Vy / Vx => A = Tan^-1 A (Vy / Vx)

Where A is used as angle instead of theta in diagram

Example calculation involving projectile motion:

1. A body is projected with a velocity of 200m/s at and angle of 30 °C to the horizontal.

• Calculate the time taken to reach its maximum height.
• Calculate its velocity after 16 seconds.

Answers:

• Finding the time for maximum height.

angle A = 30 °C
          V = 200m/s
Acceleration(a) = -10 m/s²
Vy = 0 m/s

Therefore Uy = VsinA                                                [ Note: Uy represents initial velocity]

                  Uy = 200 x Sin 30

                  Uy = 100 m/s

                  

                  Vy = Uy = at

                  Vy - Uy = at

                        a

                   0 - 100 = t

                      - 10

                      10 sec = t

Therefore Maximum Time (t) = 10 seconds

• Finding the velocity after 16 seconds.

                  Vx = V cos A 
                  Vx = 200 x Cos 30
                  Vx = 173.2 m/s

                  Vy = Uy + at
                  Vy = 100 - 10 (16)
                  Vy = -60 m/s

Therefore V =  √[Vy^2 + Vx^2]
                      =  √[(-60)^2 + (173.2)^2]
                      =  √33598
                      =  183.30 m/s