Projectile Motion

Projectile motion refers to the motion of an object that is projected into the air at an angle to the horizontal.


  • Acceleration due to gravity, g, is constant (9.81 $\text{m s}^{-2}$) over entire motion and is always directed downwards.
  • No horizontal acceleration
  • Effect of air resistance is negligible


Path of projectile without air resistance (always a parabola)

Taking upwards as positive, (Click on image to enlarge)

Projectile motion with air resistance

Key Characteristics of Graph:

  • Horizontal range of object is shorter
  • Maximum height reached is smaller
  • Path is asymmetrical about highest point


  • Horizontal velocity no longer constant
  • Horizontal velocity decreases with time. Object slows down
  • Smaller horizontal range


  • Going up, $a_{\text{upwards}} \, = \, g + \frac{F_{\text{Drag} \, \text{Force}}}{m}$
  • Going down, $a_{\text{downwards}} \, = \, g-\frac{F_{\text{Drag} \, \text{Force}}}{m}$

Since $\mid a_{\text{upwards}} \mid \, > \, \mid a_{\text{downwards}} \mid$, $\Delta V_{\text{upwards}} \, > \, \Delta V_{\text{downwards}}$. So, object slows down at a faster rate on the way up, time taken to reach maximum point is less than the time taken to reach the ground from the maximum point.

Simulations of projectile motion:

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4 thoughts on “Projectile Motion”

  1. I need to know what if the air resistance is not neglected Will The optimum angle be greater or less than 45 degrees

  2. a canon ball is project so as to attain a maximum range. Find the maximum height attained if the initial velocity is U. pls can someone help with this question

    • Nope. Taking upwards as positive means:
      – upwards displacement from reference point is positive,
      – moving in the upwards direction is positive (positive velocity),
      – accelerating in the upwards direction is positive.

      Hope this clarifies.


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