Student handout: Projectile with Linear Drag

Theoretical Mechanics 2020
Students consider projectile motion of an object that experiences drag force that in linear with the velocity. Students consider the horizontal motion and the vertical motion separately. Students solve Newton's 2nd law as a differential equation.
What students learn
  • Practice solving separable differential equations
  • Identify terminal speed \(|\vec{v}_{term}|=mg/b\)
  • Horizontal motion is bounded
  • Practice checking dimensions, considering limiting cases, and resolving graphs and equations

A ping pong ball is thrown from the roof of Weniger Hall with an initial velocity that makes an angle \(\theta\) up from horizontal. The ball experiences a drag force that is proportional to its velocity.

Use Newton's 2nd Law to solve for the position of the ping pong ball for any value of time.

Hints:

  • Consider the horizontal and vertical components of the motion separately.
  • While you're planning and working on your solution, be prepared to answer the following questions:
    1. What are you doing right now?
    2. How will the result help you?
    3. How are you checking that the result is sensible?

Keywords
Projectile Motion Drag Forces Newton's 2nd Law Separable Differential Equations
Learning Outcomes