How Long Does It Take a Raindrop to Reach 63% of Its Terminal Velocity?

[peweee17]

Homework Statement

The terminal velocity of a 2×10−5 kg raindrop is about 7m/s. Assuming a drag force Fd= - bv,
Assuming a drag force determine the time required for such a drop, starting from rest, to reach 63% of terminal velocity.

Homework Equations

Fd=-bv
Sum of F-ma

The Attempt at a Solution

I use Fd=-bv to solve for b then used Fd-Fg=ma and reduced that to dv/dt=-g-(bv/m) but don't know how to determine time.

 

[cristo]

You need to show some work before we can help you: what have you tried?

 

[baba89]

To determine the time required for the raindrop to reach 63% of its terminal velocity, we can use the equation for velocity with respect to time under constant acceleration:

v = v0 + at

Where v is the final velocity (in this case, 63% of the terminal velocity), v0 is the initial velocity (which is 0 since the raindrop starts from rest), a is the acceleration (which is the acceleration due to gravity, -9.8 m/s^2), and t is the time we are trying to find.

We can rewrite the equation to solve for t:

t = (v - v0)/a

Substituting in the values given in the problem, we get:

t = (0.63 * 7 m/s - 0 m/s)/(-9.8 m/s^2) = 0.045 seconds

Therefore, it would take approximately 0.045 seconds for the raindrop to reach 63% of its terminal velocity.