Block sliding down 30° incline with friction and air resistance

[frenika]

Problem: A 64-lb block is released from the top of a plane inclined at 30 degrees to the horizontal. As the block slides down the plane, its coefficient of friction is 0.25, and it experiences a drag force due to air resistance equal to one-half is velocity in ft/sec. (a) Determine the equation for the velocity of the block. (b) Determine the equation for the displacement of the block, (c) Calculate the displacement and velocity of the block 5 sec after it is released.

 

[Doc Al]

You also posted this question here: https://www.physicsforums.com/showthread.php?t=23079

 

[frenika]

I understand the formulas for the force and everything but I need help setting up the differential equation

 

[gnome]

After you have expressions for each of the forces and for the acceleration, write
$$F = ma$$
Then, beneath that, in the corresponding positions, rewrite it using the expressions you found. That will give you the differential equation you have to solve.