How Does a Skydiver's Velocity Change with Distance After Parachute Deployment?

[Will Freedic]

Homework Statement

A sky driver reaches his terminal velocity of 373 ms^-1 and deploys his parachute at a height of 1500m, the drag force =bv^2 and weigh can be ignored. Find an expression for velocity as a function of distance traveled from the point the parachute was deployed

The Attempt at a Solution

I can find velocity as a function of time easy enough but not a function of distance[/B]

 

[BvU]

Hi Will,

Please read the guidelines, use the template, don't delete parts of the template, show your work so far and we'll help you from the point where you get stuck.

 

[SteamKing]

Homework Statement

A sky driver reaches his terminal velocity of 373 ms^-1 and deploys his parachute at a height of 1500m, the drag force =bv^2 and weigh can be ignored. Find an expression for velocity as a function of distance traveled from the point the parachute was deployed

A terminal velocity of 373 m/s is quite a feat. It's also greater than Mach 1, which makes it unlikely to occur. Are you sure a decimal point hasn't been misplaced?

 

[haruspex]

There is a standard trick for eliminating time from an acceleration equation.
$a=\frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=v\frac{dv}{dx}$.
Note that if we apply this to F=ma and integrate wrt x we get $\int F.dx=\frac 12 mv^2$.

 

[Will Freedic]

Thank you!, so is it correct to say that:

Cv² = ma
cv² = mv dvdx.
Cm/x = v² / 2 + c
Cheers

 

[haruspex]

Thank you!, so is it correct to say that:

Cv² = ma
cv² = mv dvdx.
Cm/x = v² / 2 + c
Cheers

A couple of problems there. First, what happened to gravity? Secondly, I don't understand what you did to get from cv² = mv dvdx (presumably you meant mv dv/dx) to Cm/x = v² / 2 + c

 

[Will Freedic]

A couple of problems there. First, what happened to gravity? Secondly, I don't understand what you did to get from cv² = mv dvdx (presumably you meant mv dv/dx) to Cm/x = v² / 2 + c

Thank you for your help, i am new to these forums so am a little slow!, managed to get there now tho