SOLUTION: an object of mass 3kg is released from rest at 500m above ground, and allowed to fall under influence of gravity. the force due to air resistance is proportional to the velocity of

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: an object of mass 3kg is released from rest at 500m above ground, and allowed to fall under influence of gravity. the force due to air resistance is proportional to the velocity of      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1051000: an object of mass 3kg is released from rest at 500m above ground, and allowed to fall under influence of gravity. the force due to air resistance is proportional to the velocity of the object with k=3N sec/m. formulate the particular explicit solution of the problem
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You have the force of gravity acting towards the earth.
You have the force of air resistance acting in the opposite direction.
So summing the forces,
m%28dv%2Fdt%29=-g%2Bkv
3%28dv%2Fdt%29-3v=-9.8 with v%5B0%5D=0
Solving that gives you,
v%28t%29=%289.8%2F3%29%281-e%5E%28t%29%29
Now you have an equation for the velocity of the object.
Integrate to get the equation for position,
x%28t%29=%289.8%2F3%29%28t-e%5E%28t%29%29%2BC with initial condition x%280%29=500
%289.8%2F3%29%280-1%29%2BC=500
C=500%2B9.8%2F3
C=1509.8%2F3
So then,
x%28t%29=%289.8%2F3%29%28t-e%5E%28t%29%29%2B1509.8%2F3