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## Main Question or Discussion Point

Hi All -

2nd year in my teaching career and already I'm teaching an AP C: Mechanics course! As I'm creating my midterm for my students, I'm looking at AP Free Response questions to give them practice for the real thing. As we're only 8 units in, my selections are limited to Work, Energy, Dynamics, and Kinematics essentially. That said, I've found what I find to be a great resistive motion problem.

The exam is on AP's website http://apcentral.collegeboard.com/apc/members/repository/physics_c_m_00.pdf".

My problem is concerning the last part of Question 2 in the Mechanics section. It reads "Determine the energy dissipated by the drag force during the fall if the ball is released at height

I can easily see how my students would produce the answer of "Energy dissipated is what would be predicted by conservation of energy - what is actually there" or "mgh - 1/2mv

Can anyone help?

2nd year in my teaching career and already I'm teaching an AP C: Mechanics course! As I'm creating my midterm for my students, I'm looking at AP Free Response questions to give them practice for the real thing. As we're only 8 units in, my selections are limited to Work, Energy, Dynamics, and Kinematics essentially. That said, I've found what I find to be a great resistive motion problem.

The exam is on AP's website http://apcentral.collegeboard.com/apc/members/repository/physics_c_m_00.pdf".

My problem is concerning the last part of Question 2 in the Mechanics section. It reads "Determine the energy dissipated by the drag force during the fall if the ball is released at height

*h*and reaches its terminal speed before hitting the ground, in terms of the given quantities and fundamental constants"I can easily see how my students would produce the answer of "Energy dissipated is what would be predicted by conservation of energy - what is actually there" or "mgh - 1/2mv

^{2}. My problem is with the second way to find the solution as Work = integral F dot dr. If the force is given by bv^{2}then we are integrating bv^{2}. However, the velocity should change with respect to height, so this is no easy integral. I'm struggling to see how to approach the integral without finding a function v(x).Can anyone help?

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