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

                    

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      6 Response to Projectile Motion and Example Calculations

      March 15, 2011 at 6:17 AM

      Thanks for such an easy explanation!

      March 15, 2011 at 8:00 AM

      Really clear way of explaining such a complex topic!

      March 16, 2011 at 3:43 AM

      Nice explanation. It's important to understand this because, later, you'll move on to pendlums, springs, turbine blades, pump impellers, whirlpools, and cloud movement (unless you branch off into medicine or finance).

      March 17, 2011 at 8:43 AM

      It is always very nice to come to this blog as it is very didactic.

      April 5, 2011 at 8:06 AM

      Thanks for sharing with us these calculation examples. They are really useful.

      July 24, 2012 at 9:36 PM

      A bullet is fired at such an angle such that the horizontal displacement is 3 times the maximum height reached by the bullet.The initial velocity of the bullet is 150m/s.Calculte the angle of projection.

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