a ball with mass 0.15 kg is thrown upward with initial velocity 20 m/sec from the roof of a building 30 m high. there is a force due to air resistance of |v|/30, where velocity v is measured in m/sec.

Question

a ball with mass 0.15 kg is thrown upward with initial velocity 20 m/sec from the roof of a building 30 m high. there is a force due to air resistance of |v|/30, where velocity v is measured in m/sec. 
a. find the maximum height above the ground the ball reaches. 
b. find the time the ball hits the ground.

you cannot use the kinematic equations... you must use calculus.  (which means you can't use average velocity!)

drwls · Answer

I answered this already by an approximate method. If you want to use differential equations, you are on your own. A numerical integration, using small time intervals and recalculating v, friction and incremental motion each time, would be much easier. A computer spreadsheet could be used.