- #1
Jamin2112
- 986
- 12
Homework Statement
The velocity v(t) of a skydiver falling to the ground is governed by
m(dv/dt)=mg-kv2,
where m is the skydiver's mass, g is the acceleration due to gravity, k > 0 is the drag coefficient, and v(t)≥0.
(a) Solve this equation for v(t) with the initial condition v(0).
Homework Equations
The Attempt at a Solution
Divide m throughout
==> dv/dt = g - (k/m)v2
Factor out a k/m
dv/dt = k/m (mg/k - v2)
Separate
dv / (mg/k - v2) = (k/m)dt
Now I have it in the form ∫ dx/(a2-x2) = (1/2a)ln[(a+x)/(a-x)], with a = √(mg/k) and x=v, obviously.
==> [1/√(mg/k)] ln[ (√(mg/k) + v) / (√(mg/k) - v)] = (k/m)t + C
..... and this all seems far too complicated.
Suggestions, please.