# 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.

Homework Helper
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 travelled 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.

Homework Helper
Integrating v(t) would give me the total meters travelled 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?