A body of mass 10 slugs is dropped from a height of 1000ft with no initial velocity. The body encounters an air resistance proportional to its velocity. If the limiting velocity is known to be 320ft/s, find an expression for the velocity of the body at any time t, an expression for the position of the body at any time t, and the time required for the body to attain a velocity of 160ft/s.

Question

A body of mass 10 slugs is dropped from a height of 1000ft with no initial velocity.  The body encounters an air resistance proportional to its velocity.  If the limiting velocity is known to be 320ft/s, find an expression for the velocity of the body at any time t, an expression for the position of the body at any time t, and the time required for the body to attain a velocity of 160ft/s.

anonymous · Answer

You can use Newton's Second Law and put the resistance = mav for some constant a. Then derive the equation of motion since acceleration = dv/dt.

anonymous · Answer

Take into account that Force over the body (FB)=Gravitational Force(GF)-Air resistance(AR). If the Air Resistance is proportional to its velocity, then AR=k·V, then we have:
FB=m·dV/dt;GF=m·g;AR=k·V and the expression: FB=GF-AR can be put as:
m·dV/dt=m·g-k·V or m·dV/dt+k·V=m·g
Tell me if you know how to solve this differential equation