Question

Is there a formula to calculate the minimun height that is require for an object to reach terminal velocity?

we know the terminal velocity .778499 m/s, the time it takes for the object to reach terminal velocity .33s, and the weight of the object.0045kg.

Answer 1

we know F_drag = -k*v

-m*g = -k*v

==> k = m*g/v

= 0.0045*9.8/0.778499

= 0.0566 N.s/m

Impulse = change in momentum

integral F*dt

integral (m*g - k*v)*dt = 0.0045*0.778400

m*g*t - integral k*(dy/dt)*dt = 0.0045*0.778400

m*g*t - integral k*dy = 0.0045*0.778400

m*g*t - k*y = 0.0045*0.778400

k y = m*g*t - 0.0045*0.778400

y = (m*g*t - 0.0045*0.778400)/k

= (0.0045*9.8*0.33 - 0.0045*0.778400)/0.0566

= 0.195 m or 19.5 cm <<<<<<<------------Answer