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.
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:
- What are you doing right now?
- How will the result help you?
- How are you checking that the result is sensible?
This problem is too long to do in one go. I like to
If you want to skips parts, skip position and just ask for velocity.
Separating the Vertical Component of Velocity: Many students have trouble separating the differential equation for the vertical components of the velocity. They want to keep separate the drag and gravity.
\begin{align*} \frac{dv_y}{dt} +\frac{b}{m}v_y = -g \end{align*}