Calculating Time of Free Fall Using Distance and Time Integrals

[armolinasf]

Homework Statement

If you jump out of an airplane and your parachute fails to open our downward velocity t seconds after jumping is approximated for g=9.8m/sec^2 and k=.2 sec, by

v(t)=(g/k)(1-e^(-kt))


So, if you jump from 5000 meters above the ground write an equation whose solution is the number of seconds you fall before hitting the ground.

The Attempt at a Solution

This is coming from the section in my book on definite integrals but I'm not sure where to start. Thanks for any help.

 

[Dick]

v(t)=x'(t) where x(t) is the vertical displacement. So to find x(t) given v(t) you would integrate v(t), right?

 

[armolinasf]

Integrating v(t) would give me the total meters traveled but if I'm looking for the number of seconds it took to fall 5000 meters I would need to integrate something else.

Or could I use the integral that gives me distance and say that t=d/v where d is the integral and v is v(t)? This was my first thought but I'm uncertain since v(t) is a function of time.

 

[Dick]

Integrating v(t) would give me the total meters traveled but if I'm looking for the number of seconds it took to fall 5000 meters I would need to integrate something else.

Or could I use the integral that gives me distance and say that t=d/v where d is the integral and v is v(t)? This was my first thought but I'm uncertain since v(t) is a function of time.

If you can find x(t) you can certainly try and solve x(t)=5000 for t, right? Using d/v is wrong. The speed isn't constand.

 

[armolinasf]

So then finding x(t) would just be finding the antiderivative of v(t) correct?

 

[Dick]

Sure.