Solve Raindrop Problem: Determine Time to Reach 63% Terminal Velocity

[siwik39]

Homework Statement

The terminal velocity of a 0.000038 kg raindrop is about 14 m/s.

(a) Assuming a drag force FD = -bv, determine the value of the constant b.
correct check mark kg/s

(b) Determine the time required for such a drop, starting from rest, to reach 63 percent of terminal velocity.


2. The attempt at a solution

I got part a by myself, where b= 0.0000266 kg/s

Part b has given me some trouble. I drew a diagram and set the the equation
F=ma=mg - (-bv) Then i tried solving for a, and using that to find t. However, I realized you can't use a=Vf-Vi/t because a is not constant. I have never done an equation like this with t and a non-constant a. I really don't want the answer because I won't learn anything, but any help or hints would be appreciated.

 

[tiny-tim]

Welcome to PF!

… Assuming a drag force FD = -bv
…
F=ma=mg - (-bv)

Hi siwik39! Welcome to PF!

Isn't it ma=mg + (-bv)?

Anyway, just put a = dv/dt, and solve for v.

 

[siwik39]

I got part a. I was trying to solve for t. But thanks I got it with the dv/dt.